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Math Gr 8 Term 3 Test
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Math Gr 8 Term 3 Test

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Questions and Answers

What is the definition of an equation?

  • A mathematical statement that asserts the equality of two expressions. (correct)
  • A mathematical statement that asserts the equality of three expressions.
  • A mathematical statement that asserts the inequality of three expressions.
  • A mathematical statement that asserts the inequality of two expressions.

    • What is solving an equation?

  • Finding the value(s) of the variable(s) that make the equation true. (correct)
  • Finding the value(s) of the constant(s) that make the equation true.
  • Finding the value(s) of the expression(s) that make the equation false.
  • Finding the value(s) of the variable(s) that make the equation false.

    • What are additive inverses?

  • Numbers that subtract to give one.
  • Numbers that divide to give zero.
  • Numbers that multiply to give one.
  • Numbers that add up to zero. (correct)

    • What is the process of solving an equation by finding the original value of the variable that produces a given result?

    <p>Undoing</p> Signup and view all the answers

    What is the sum of angles that form on a straight line?

    <p>180°</p> Signup and view all the answers

    What are two angles that add up to 180° called?

    <p>Supplementary angles</p> Signup and view all the answers

    What is the formula for angles on a straight line?

    <p>∠1 + ∠2 + ∠3 = 180°</p> Signup and view all the answers

    What can be said about adjacent supplementary angles if two lines are perpendicular?

    <p>They are each 90°</p> Signup and view all the answers

    What is the key property of vertically opposite angles?

    <p>They are always equal.</p> Signup and view all the answers

    What type of angles are formed when a transversal intersects two lines, and lie on the same side of the transversal and between the two lines?

    <p>Co-interior angles</p> Signup and view all the answers

    What is the sum of the interior angles of a quadrilateral?

    <p>360</p> Signup and view all the answers

    What is the relationship between corresponding angles when two lines are parallel and intersected by a transversal?

    <p>They are equal</p> Signup and view all the answers

    What type of triangle has two sides and two angles that are equal?

    <p>Isosceles triangle</p> Signup and view all the answers

    What is the formula for alternate interior angles when two lines are parallel and intersected by a transversal?

    <p>$\angle a = \angle e$</p> Signup and view all the answers

    What is the key property of co-interior angles when two lines are parallel and intersected by a transversal?

    <p>They are supplementary</p> Signup and view all the answers

    What type of quadrilateral has four equal sides and four right angles?

    <p>Square</p> Signup and view all the answers

    What is the relationship between alternate exterior angles when two lines are parallel and intersected by a transversal?

    <p>They are equal</p> Signup and view all the answers

    What is the formula for vertically opposite angles?

    <p>$\angle a = \angle c$</p> Signup and view all the answers

    What is the definition of a rhombus?

    <p>A quadrilateral with all sides equal and opposite equal angles</p> Signup and view all the answers

    What is the name of the line segment within a circle that touches two points?

    <p>Chord</p> Signup and view all the answers

    What is the process of creating precise figures using specific tools and methods?

    <p>Construction of shapes</p> Signup and view all the answers

    What is the name of the technique used to divide an angle into two equal parts?

    <p>Bisecting an angle</p> Signup and view all the answers

    What is the name of the region bounded by two radii and an arc?

    <p>Sector</p> Signup and view all the answers

    What is the primary tool used to draw a circle with a given radius?

    <p>Compass</p> Signup and view all the answers

    What is the name of the polygon with all sides and angles equal?

    <p>Regular polygon</p> Signup and view all the answers

    What is the process of creating a line perpendicular to a given line?

    <p>Constructing a perpendicular bisector</p> Signup and view all the answers

    What is the term for the distance around a circle?

    <p>Circumference</p> Signup and view all the answers

    What is the name of the technique used to construct a quadrilateral by drawing the diagonals and ensuring they intersect at the correct angles?

    <p>Using diagonals</p> Signup and view all the answers

    What is the primary criterion for determining if two shapes are similar?

    <p>Having the same shape and proportionality of corresponding sides</p> Signup and view all the answers

    What is the purpose of finding the scale factor between similar shapes?

    <p>To find the unknown side lengths or scale shapes up or down</p> Signup and view all the answers

    When solving problems involving similar shapes, what should you check for in the corresponding angles and sides?

    <p>Equality of corresponding angles and proportionality of corresponding sides</p> Signup and view all the answers

    What is the advantage of using similarity in real-world applications?

    <p>It enables the creation of proportional models and structures</p> Signup and view all the answers

    What is the key to solving problems involving composite figures with similar and congruent shapes?

    <p>Breaking down the figure into simpler components</p> Signup and view all the answers

    What is the role of geometric proofs in similarity and congruence?

    <p>To develop logical arguments to establish relationships between different parts of geometric figures</p> Signup and view all the answers

    What is the purpose of identifying similar shapes in a problem?

    <p>To apply the properties of similar shapes to solve the problem</p> Signup and view all the answers

    What is a common application of similarity in real-world problems?

    <p>Map reading</p> Signup and view all the answers

    What is the sum of the interior angles of a quadrilateral?

    <p>360°</p> Signup and view all the answers

    What is the characteristic of a parallelogram?

    <p>Opposite sides equal and parallel</p> Signup and view all the answers

    What is the angle subtended by an arc at the center of a circle?

    <p>Twice the angle subtended at any point on the circumference</p> Signup and view all the answers

    What is the property of a cyclic quadrilateral?

    <p>Opposite angles sum to 180°</p> Signup and view all the answers

    What is the Pythagorean theorem used for?

    <p>Solving problems involving right triangles</p> Signup and view all the answers

    What is the property of a rhombus?

    <p>All sides equal, diagonals bisect each other at right angles</p> Signup and view all the answers

    What is the result of translating a shape?

    <p>The shape remains the same size and shape</p> Signup and view all the answers

    What is the definition of a trapezium?

    <p>A quadrilateral with one pair of opposite sides parallel</p> Signup and view all the answers

    What is the characteristic of a rectangle?

    <p>Opposite sides equal, all angles 90°</p> Signup and view all the answers

    What is the sum of the interior angles of a triangle?

    <p>180°</p> Signup and view all the answers

    What is the primary objective of the 'Understand the Problem' step in problem-solving?

    <p>To identify the geometric figures involved in the problem</p> Signup and view all the answers

    What is the definition of congruent shapes?

    <p>Two shapes with the same shape and size</p> Signup and view all the answers

    What is the Side-Angle-Side (SAS) criterion for congruent triangles?

    <p>If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle</p> Signup and view all the answers

    What is the definition of similar shapes?

    <p>Two shapes with the same shape but not necessarily the same size</p> Signup and view all the answers

    What is the Angle-Angle (AA) criterion for similar triangles?

    <p>If two angles of one triangle are equal to two angles of another triangle</p> Signup and view all the answers

    What is the primary purpose of the 'Solve for Unknowns' step in problem-solving?

    <p>To perform algebraic manipulations to find the values of unknown measurements</p> Signup and view all the answers

    What is the primary objective of the 'Verify Solutions' step in problem-solving?

    <p>To check the solutions by substituting back into the original conditions</p> Signup and view all the answers

    Which of the following is a real-world application of congruent shapes?

    <p>Creating tiling designs</p> Signup and view all the answers

    What is the primary objective of the 'Draw Diagrams' step in problem-solving?

    <p>To sketch accurate diagrams to visualize the problem</p> Signup and view all the answers

    What is the primary objective of the 'Apply Theorems and Properties' step in problem-solving?

    <p>To use relevant geometric theorems and properties to set up equations or logical statements</p> Signup and view all the answers

    When two lines intersect, what is the relationship between the vertically opposite angles?

    <p>They are equal</p> Signup and view all the answers

    What is the name of the line that intersects at least two other lines?

    <p>Transversal</p> Signup and view all the answers

    What type of angles are formed when a transversal intersects two lines, and lie outside the two lines on opposite sides of the transversal?

    <p>Alternate exterior angles</p> Signup and view all the answers

    What is the sum of the interior angles of any quadrilateral?

    <p>360°</p> Signup and view all the answers

    What type of triangle has all sides and angles equal?

    <p>Equilateral triangle</p> Signup and view all the answers

    What is the relationship between co-interior angles when two lines are parallel and intersected by a transversal?

    <p>They are supplementary</p> Signup and view all the answers

    What type of quadrilateral has four equal sides and four right angles?

    <p>Square</p> Signup and view all the answers

    What is the formula for corresponding angles when two lines are parallel and intersected by a transversal?

    <p>∠a = ∠e</p> Signup and view all the answers

    What is the relationship between alternate interior angles when two lines are parallel and intersected by a transversal?

    <p>They are equal</p> Signup and view all the answers

    What is the formula for alternate exterior angles when two lines are parallel and intersected by a transversal?

    <p>∠a = ∠g</p> Signup and view all the answers

    What is the purpose of solving an equation?

    <p>To find the value of the variable that makes the equation true</p> Signup and view all the answers

    What is the relationship between the angles formed on a straight line?

    <p>They add up to 180°</p> Signup and view all the answers

    What is the purpose of using additive inverses when solving an equation?

    <p>To move constants to the other side of the equation</p> Signup and view all the answers

    What is the term for the process of finding the original value of the variable that produces a given result?

    <p>Undoing</p> Signup and view all the answers

    What is the relationship between two equations that have the same solution?

    <p>They are equivalent</p> Signup and view all the answers

    What is the purpose of using multiplicative inverses when solving an equation?

    <p>To solve for the variable</p> Signup and view all the answers

    What is the result of evaluating an expression by substituting a variable with a value?

    <p>Doing</p> Signup and view all the answers

    What is the purpose of setting up an equation?

    <p>To make a mathematical statement</p> Signup and view all the answers

    What is the primary objective of using theorems and proofs in geometry?

    <p>To prove properties of geometric figures and validate theoretical findings</p> Signup and view all the answers

    What is the key property of a cyclic quadrilateral?

    <p>Its opposite angles sum to 180°</p> Signup and view all the answers

    What is the purpose of using geometric transformations in problem-solving?

    <p>To change the position or size of a geometric shape while preserving its properties</p> Signup and view all the answers

    What is the characteristic of a square?

    <p>All sides are equal, and all angles are 90°</p> Signup and view all the answers

    What is the result of reflecting a shape over a line of symmetry?

    <p>The shape remains unchanged</p> Signup and view all the answers

    What is the key characteristic of a kite?

    <p>It has two pairs of adjacent equal sides</p> Signup and view all the answers

    Which geometric shape has a line segment within the circle that touches two points?

    <p>Circle</p> Signup and view all the answers

    What is the angle subtended by an arc at the center of a circle?

    <p>Twice the angle subtended at the circumference</p> Signup and view all the answers

    What is the primary focus of constructing 2D shapes?

    <p>Creating accurate shapes and angles</p> Signup and view all the answers

    What is the purpose of identifying congruent and similar shapes in geometry?

    <p>To solve problems involving unknown angles and side lengths</p> Signup and view all the answers

    What is the name of the technique used to divide an angle into two equal parts?

    <p>Bisecting an angle</p> Signup and view all the answers

    What is the primary objective of the 'Understand the Problem' step in problem-solving?

    <p>To identify the key concepts and formulas required to solve the problem</p> Signup and view all the answers

    What is the characteristic of a convex polygon?

    <p>All interior angles are less than 180 degrees</p> Signup and view all the answers

    What is the characteristic of a parallelogram?

    <p>Opposite sides are equal and parallel</p> Signup and view all the answers

    What is the purpose of using geometric tools in problem-solving?

    <p>To construct and measure geometric shapes accurately</p> Signup and view all the answers

    What is the name of the region bounded by a chord and an arc?

    <p>Segment</p> Signup and view all the answers

    What is the purpose of identifying properties of geometric figures?

    <p>To investigate relationships between shapes</p> Signup and view all the answers

    What is the key characteristic of a parallelogram?

    <p>Opposite sides are equal and parallel</p> Signup and view all the answers

    What is the name of the technique used to construct a 60° angle?

    <p>Drawing an equilateral triangle</p> Signup and view all the answers

    What is the primary tool used to draw a circle with a given radius?

    <p>Compass</p> Signup and view all the answers

    What is the primary step in solving problems involving geometric shapes?

    <p>Draw diagrams to visualize the problem</p> Signup and view all the answers

    What is the key property of congruent shapes?

    <p>Corresponding sides and angles are equal</p> Signup and view all the answers

    What is the Side-Side-Side (SSS) criterion for congruent triangles?

    <p>If all three sides of one triangle are equal to all three sides of another triangle</p> Signup and view all the answers

    What is the purpose of using similarity in real-world applications?

    <p>To scale shapes up or down to a desired size</p> Signup and view all the answers

    What is the result of translating a shape?

    <p>A shape with a different size and orientation</p> Signup and view all the answers

    What is the primary objective of the 'Apply Theorems and Properties' step in problem-solving?

    <p>To set up equations or logical statements</p> Signup and view all the answers

    What is the key property of similar shapes?

    <p>Corresponding angles are equal, and corresponding sides are in proportion</p> Signup and view all the answers

    What is the purpose of identifying congruent shapes in a problem?

    <p>To apply the properties of congruent shapes to solve the problem</p> Signup and view all the answers

    What is the primary criterion for determining if two shapes are similar?

    <p>The Angle-Angle (AA) criterion</p> Signup and view all the answers

    What is the advantage of using congruent shapes in problem-solving?

    <p>It enables the application of properties of congruent shapes</p> Signup and view all the answers

    What is the primary purpose of identifying similar shapes in a problem?

    <p>To apply the properties of similar shapes to solve the problem</p> Signup and view all the answers

    When solving problems involving similar shapes, what should you check for in the corresponding angles and sides?

    <p>Equality of corresponding angles and proportionality of corresponding sides</p> Signup and view all the answers

    What is the advantage of using similarity in real-world applications?

    <p>It enables the creation of proportional models and structures</p> Signup and view all the answers

    What is the key to solving problems involving composite figures with similar and congruent shapes?

    <p>Breaking down the complex figure into simpler components</p> Signup and view all the answers

    What is the role of geometric proofs in similarity and congruence?

    <p>To develop logical arguments to establish relationships between geometric figures</p> Signup and view all the answers

    What is the purpose of finding the scale factor between similar shapes?

    <p>To calculate unknown side lengths</p> Signup and view all the answers

    What should you use to determine if two shapes are similar?

    <p>Any of the above</p> Signup and view all the answers

    What is the primary objective of the 'Use Properties of Similar Shapes' step in problem-solving?

    <p>To use the proportionality of corresponding sides to find missing lengths</p> Signup and view all the answers

    What is the minimum number of sides required to construct a polygon with a cyclic quadrilateral?

    <p>4</p> Signup and view all the answers

    If a triangle has one right angle, what is the maximum number of acute angles it can have?

    <p>2</p> Signup and view all the answers

    What is the relationship between the sum of the interior angles of a quadrilateral and the sum of the interior angles of a triangle?

    <p>The sum of the interior angles of a quadrilateral is three times the sum of the interior angles of a triangle.</p> Signup and view all the answers

    What is the characteristic of a quadrilateral with all sides and angles equal?

    <p>It is a square.</p> Signup and view all the answers

    What is the maximum number of lines of symmetry a rectangle can have?

    <p>4</p> Signup and view all the answers

    What is the formula for alternate interior angles when two lines are parallel and intersected by a transversal?

    <p>∠a = ∠e</p> Signup and view all the answers

    If a circle has a central angle of 60 degrees, what is the measure of the arc subtended by this angle?

    <p>120 degrees</p> Signup and view all the answers

    What is the minimum number of transformations required to turn a triangle into its mirror image?

    <p>2</p> Signup and view all the answers

    What is the relationship between the angles formed by a transversal intersecting two parallel lines?

    <p>Corresponding angles are equal, and alternate angles are equal.</p> Signup and view all the answers

    What is the key property of co-interior angles when two lines are parallel and intersected by a transversal?

    <p>They are supplementary.</p> Signup and view all the answers

    What is the maximum number of diagonals a quadrilateral can have?

    <p>6</p> Signup and view all the answers

    What is the characteristic of a triangle with two sides and two angles that are equal?

    <p>It is an isosceles triangle.</p> Signup and view all the answers

    If a triangle has two sides of equal length, what is the minimum number of isosceles triangles it can be part of?

    <p>1</p> Signup and view all the answers

    What is the formula for vertically opposite angles?

    <p>∠a = ∠c</p> Signup and view all the answers

    What is the maximum number of axes of symmetry a rhombus can have?

    <p>4</p> Signup and view all the answers

    If a triangle has a right angle, what is the minimum number of angles that can be acute?

    <p>1</p> Signup and view all the answers

    What is the key property of alternate exterior angles when two lines are parallel and intersected by a transversal?

    <p>They are equal.</p> Signup and view all the answers

    What is the relationship between corresponding angles when two lines are parallel and intersected by a transversal?

    <p>They are equal.</p> Signup and view all the answers

    What is the maximum number of rotations a shape can have to coincide with its original position?

    <p>6</p> Signup and view all the answers

    What is the characteristic of a quadrilateral with opposite sides that are equal and four right angles?

    <p>It is a rectangle.</p> Signup and view all the answers

    What is the advantage of using inverses when solving equations?

    <p>It allows for the isolation of the variable, making it easier to find the solution.</p> Signup and view all the answers

    What is the relationship between the angles on a straight line?

    <p>The sum of the angles is always 180°.</p> Signup and view all the answers

    What is the purpose of doing and undoing when solving equations?

    <p>To isolate the variable and find the original value.</p> Signup and view all the answers

    What is the role of additive inverses in solving equations?

    <p>To move constants to the other side of the equation.</p> Signup and view all the answers

    What is the key concept in solving equations using inverses?

    <p>Isolating the variable using additive and multiplicative inverses.</p> Signup and view all the answers

    What is the relationship between the angles formed by two lines intersected by a transversal?

    <p>The angles are always supplementary.</p> Signup and view all the answers

    What is the purpose of thinking forwards and backwards when solving equations?

    <p>To evaluate the expression and find the original value.</p> Signup and view all the answers

    What is the advantage of using equivalent equations?

    <p>It provides an alternative method for solving equations.</p> Signup and view all the answers

    What is the minimum number of sides required to identify a shape as a polygon?

    <p>3</p> Signup and view all the answers

    Which quadrilateral has opposite sides that are equal and parallel with opposite equal angles?

    <p>Parallelogram</p> Signup and view all the answers

    What is the term for the region bounded by a chord and an arc in a circle?

    <p>Segment</p> Signup and view all the answers

    Which tool is used to create a precise angle in a geometric construction?

    <p>Compass</p> Signup and view all the answers

    What is the process of dividing an angle into two equal parts called?

    <p>Bisecting</p> Signup and view all the answers

    What is the name of the polygon with all sides and angles equal?

    <p>Regular Polygon</p> Signup and view all the answers

    Which technique is used to construct a perpendicular line to a given line?

    <p>Perpendicular bisector</p> Signup and view all the answers

    What is the term for the distance from the center of a circle to any point on the circle?

    <p>Radius</p> Signup and view all the answers

    Which quadrilateral has two pairs of adjacent sides that are equal with one pair of opposite equal angles?

    <p>Kite</p> Signup and view all the answers

    What is the process of creating a precise figure using specific tools and methods?

    <p>Construction</p> Signup and view all the answers

    What is the primary purpose of using the congruence criteria for triangles in problem-solving?

    <p>To identify the corresponding angles and sides of congruent shapes</p> Signup and view all the answers

    What is the key to solving problems involving composite figures with similar and congruent shapes?

    <p>Identifying the congruent shapes and applying the corresponding properties</p> Signup and view all the answers

    What is the primary advantage of using similarity in real-world applications?

    <p>It enables the scaling of shapes to different sizes while maintaining their proportions</p> Signup and view all the answers

    What is the role of geometric proofs in similarity and congruence?

    <p>To construct logical arguments to prove the similarity or congruence of shapes</p> Signup and view all the answers

    What is the primary objective of the 'Understand the Problem' step in problem-solving?

    <p>To carefully read the problem statement and identify the geometric figures involved</p> Signup and view all the answers

    What is the property of congruent shapes that enables them to be superimposed on each other perfectly?

    <p>All corresponding angles and sides are equal</p> Signup and view all the answers

    What is the primary criterion for determining if two shapes are similar in terms of corresponding angles?

    <p>All corresponding angles are equal and corresponding sides are proportional.</p> Signup and view all the answers

    What is the primary criterion for determining if two shapes are similar?

    <p>The shapes have corresponding sides that are proportional</p> Signup and view all the answers

    What is the purpose of finding the scale factor between similar shapes?

    <p>To calculate the unknown side lengths of one shape.</p> Signup and view all the answers

    What is the purpose of finding the scale factor between similar shapes?

    <p>To enable the scaling of shapes to different sizes while maintaining their proportions</p> Signup and view all the answers

    When solving problems involving similar shapes, what should you check for in the corresponding angles and sides?

    <p>Both corresponding angles are equal and corresponding sides are proportional.</p> Signup and view all the answers

    What is the advantage of using similarity in real-world applications?

    <p>It helps in creating scale models and solving practical problems.</p> Signup and view all the answers

    What is the primary advantage of using congruence in real-world applications?

    <p>It allows for the construction of precise figures</p> Signup and view all the answers

    What is the key to solving problems involving composite figures with similar and congruent shapes?

    <p>Breaking down complex figures into simpler components.</p> Signup and view all the answers

    What is the key property of similar shapes that enables them to be scaled to different sizes?

    <p>Corresponding sides are proportional</p> Signup and view all the answers

    What is the role of geometric proofs in similarity and congruence?

    <p>To establish relationships between different parts of geometric figures.</p> Signup and view all the answers

    What is the purpose of identifying similar shapes in a problem?

    <p>To solve practical problems involving similar shapes.</p> Signup and view all the answers

    What is a common application of similarity in real-world problems?

    <p>All of the above.</p> Signup and view all the answers

    If two equations have the same solution, what can be concluded about them?

    <p>They are equivalent</p> Signup and view all the answers

    What is the purpose of using additive inverses when solving an equation?

    <p>To isolate the variable</p> Signup and view all the answers

    If two angles are supplementary, what is their sum?

    <p>180°</p> Signup and view all the answers

    What is the relationship between the angles of two lines that are perpendicular?

    <p>They are each 90°</p> Signup and view all the answers

    What is the process of solving an equation by finding the value of the variable that makes the equation true?

    <p>Doing and undoing</p> Signup and view all the answers

    What is the purpose of using multiplicative inverses when solving an equation?

    <p>To solve for the variable</p> Signup and view all the answers

    What can be concluded about two angles that are equal and form on a straight line?

    <p>They are supplementary</p> Signup and view all the answers

    What is the key concept in solving equations by inspection?

    <p>Substituting a specific value of x</p> Signup and view all the answers

    What is the characteristic of a kite?

    <p>Two pairs of adjacent sides are equal with one pair of opposite equal angles</p> Signup and view all the answers

    What is the primary tool used to construct a perpendicular bisector?

    <p>Compass</p> Signup and view all the answers

    What is the characteristic of a concave polygon?

    <p>At least one interior angle is more than 180 degrees</p> Signup and view all the answers

    What is the name of the region bounded by a chord and an arc?

    <p>Segment</p> Signup and view all the answers

    What is the method of constructing a triangle given two angles and a side?

    <p>ASA or AAS</p> Signup and view all the answers

    What is the key to identifying similar shapes?

    <p>Comparing the differences and similarities in their properties</p> Signup and view all the answers

    What is the name of the angle formed by two lines intersecting at a point?

    <p>Vertically opposite angle</p> Signup and view all the answers

    What is the purpose of constructing perpendicular and parallel lines?

    <p>To create accurate shapes</p> Signup and view all the answers

    What is the characteristic of a regular polygon?

    <p>All sides and angles are equal</p> Signup and view all the answers

    What is the method of constructing a circle with a given radius?

    <p>Using a compass</p> Signup and view all the answers

    If two lines intersect, what is the relationship between the vertically opposite angles?

    <p>They are always equal</p> Signup and view all the answers

    What type of angles are formed when a transversal intersects two lines, and lie on the same side of the transversal and outside the two lines?

    <p>Alternate exterior angles</p> Signup and view all the answers

    What is the sum of the interior angles of a quadrilateral when the two lines are parallel and intersected by a transversal?

    <p>360°</p> Signup and view all the answers

    What type of triangle has all sides and angles equal?

    <p>Equilateral triangle</p> Signup and view all the answers

    What is the formula for corresponding angles when two lines are parallel and intersected by a transversal?

    <p>∠a = ∠e</p> Signup and view all the answers

    What type of quadrilateral has four equal sides and four right angles?

    <p>Square</p> Signup and view all the answers

    What is the key property of co-interior angles when two lines are parallel and intersected by a transversal?

    <p>They are always supplementary</p> Signup and view all the answers

    What type of angles are formed when a transversal intersects two lines, and lie on the same side of the transversal and inside the two lines?

    <p>Alternate interior angles</p> Signup and view all the answers

    What is the relationship between alternate exterior angles when two lines are parallel and intersected by a transversal?

    <p>They are always equal</p> Signup and view all the answers

    What is the formula for alternate interior angles when two lines are parallel and intersected by a transversal?

    <p>∠d = ∠f</p> Signup and view all the answers

    What is the key to establishing the proportionality of corresponding sides in similar shapes?

    <p>Verifying the equality of corresponding angles</p> Signup and view all the answers

    In a composite figure involving both similar and congruent shapes, what should you do to solve for unknowns?

    <p>Break down the figure into simpler components</p> Signup and view all the answers

    What is the primary purpose of developing geometric proofs in similarity and congruence?

    <p>To establish relationships between different parts of geometric figures</p> Signup and view all the answers

    In a real-world application, what is the advantage of using similarity in solving problems?

    <p>It allows for the creation of scale models</p> Signup and view all the answers

    What is the primary criterion for determining if two shapes are similar?

    <p>The AA criterion for similarity</p> Signup and view all the answers

    What is the role of the scale factor in solving problems involving similar shapes?

    <p>It is used to scale shapes up or down</p> Signup and view all the answers

    What should you check for when identifying similar shapes in a problem?

    <p>The equality of corresponding angles and proportionality of corresponding sides</p> Signup and view all the answers

    What is the purpose of using geometric proofs in solving problems involving similar and congruent shapes?

    <p>To develop logical arguments to support conclusions</p> Signup and view all the answers

    What is the minimum number of congruent triangles needed to prove that two triangles are similar?

    <p>3</p> Signup and view all the answers

    Which of the following quadrilaterals has a diagonal that bisects its opposite angles?

    <p>Rhombus</p> Signup and view all the answers

    What is the angle subtended by a semicircle at the center of the circle?

    <p>180°</p> Signup and view all the answers

    What is the result of reflecting a shape over a line of symmetry?

    <p>The original shape</p> Signup and view all the answers

    What is the minimum number of sides required to form a polygon?

    <p>3</p> Signup and view all the answers

    Which of the following is NOT a property of a kite?

    <p>All sides of equal length</p> Signup and view all the answers

    What is the angle subtended by a chord at the center of a circle?

    <p>Twice the angle subtended by the arc at the circumference</p> Signup and view all the answers

    Which of the following is an example of a cyclic quadrilateral?

    <p>Trapezium</p> Signup and view all the answers

    What is the primary objective of the problem-solving step 'Use the Facts'?

    <p>To apply theorems and properties to solve the problem</p> Signup and view all the answers

    What is the effect of a reflection on the orientation of a shape?

    <p>It changes the orientation</p> Signup and view all the answers

    What is the primary purpose of using the Side-Side-Side (SSS) criterion for congruent triangles?

    <p>To determine if two triangles have the same shape and size</p> Signup and view all the answers

    What is the key difference between congruent and similar shapes?

    <p>Congruent shapes have the same shape and size, while similar shapes have the same shape but different sizes</p> Signup and view all the answers

    What is the purpose of using diagrams in problem-solving?

    <p>To visualize the problem and identify the geometric figures involved</p> Signup and view all the answers

    What is the Angle-Angle-Side (AAS) criterion used for?

    <p>To prove that two triangles are congruent</p> Signup and view all the answers

    What is the primary advantage of using similarity in real-world applications?

    <p>It enables the creation of scale models and designs</p> Signup and view all the answers

    What is the primary objective of the 'Verify Solutions' step in problem-solving?

    <p>To check if the solution satisfies all given constraints</p> Signup and view all the answers

    What is the primary purpose of using the Right Angle-Hypotenuse-Side (RHS) criterion for congruent triangles?

    <p>To prove that two right-angled triangles are congruent</p> Signup and view all the answers

    What is the primary difference between the Side-Angle-Side (SAS) and Angle-Side-Angle (ASA) criteria for congruent triangles?

    <p>SAS involves two sides and an included angle, while ASA involves two angles and an included side</p> Signup and view all the answers

    What is the primary purpose of using the Angle-Angle (AA) criterion for similar triangles?

    <p>To prove that two triangles are similar</p> Signup and view all the answers

    What is the primary role of geometric proofs in similarity and congruence?

    <p>To construct logical arguments to show that two shapes are similar or congruent</p> Signup and view all the answers

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