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 (D)</p> Signup and view all the answers

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

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

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

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

What is the formula for angles on a straight line?

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

What is the key property of vertically opposite angles?

<p>They are always equal. (A)</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 (B)</p> Signup and view all the answers

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

<p>360 (B)</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 (C)</p> Signup and view all the answers

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

<p>Isosceles triangle (B)</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>$\angle a = \angle e$ (C)</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 (A)</p> Signup and view all the answers

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

<p>Square (C)</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 (A)</p> Signup and view all the answers

What is the formula for vertically opposite angles?

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

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

<p>Chord (D)</p> Signup and view all the answers

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

<p>Construction of shapes (B)</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 (D)</p> Signup and view all the answers

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

<p>Sector (B)</p> Signup and view all the answers

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

<p>Compass (A)</p> Signup and view all the answers

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

<p>Regular polygon (B)</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 (D)</p> Signup and view all the answers

What is the term for the distance around a circle?

<p>Circumference (D)</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 (B)</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 (A)</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 (D)</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 (D)</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 (A)</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 (C)</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 (B)</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 (C)</p> Signup and view all the answers

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

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

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

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

What is the characteristic of a parallelogram?

<p>Opposite sides equal and parallel (B)</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 (D)</p> Signup and view all the answers

What is the property of a cyclic quadrilateral?

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

What is the Pythagorean theorem used for?

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

What is the result of translating a shape?

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

What is the definition of a trapezium?

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

What is the characteristic of a rectangle?

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

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

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

What is the definition of congruent shapes?

<p>Two shapes with the same shape and size (A)</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 (B)</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 (A)</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 (C)</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 (A)</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 (A)</p> Signup and view all the answers

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

<p>Creating tiling designs (A)</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 (A)</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 (C)</p> Signup and view all the answers

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

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

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

<p>Transversal (A)</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 (A)</p> Signup and view all the answers

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

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

What type of triangle has all sides and angles equal?

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

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

<p>Square (A)</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 (A)</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 (C)</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 (D)</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 (D)</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° (D)</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 (A)</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 (A)</p> Signup and view all the answers

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

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

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

<p>Doing (A)</p> Signup and view all the answers

What is the purpose of setting up an equation?

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

What is the key property of a cyclic quadrilateral?

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

What is the characteristic of a square?

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

What is the key characteristic of a kite?

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

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

<p>Circle (B)</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 (C)</p> Signup and view all the answers

What is the primary focus of constructing 2D shapes?

<p>Creating accurate shapes and angles (D)</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 (C)</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 (C)</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 (D)</p> Signup and view all the answers

What is the characteristic of a convex polygon?

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

What is the characteristic of a parallelogram?

<p>Opposite sides are equal and parallel (D)</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 (B)</p> Signup and view all the answers

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

<p>Segment (B)</p> Signup and view all the answers

What is the purpose of identifying properties of geometric figures?

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

What is the key characteristic of a parallelogram?

<p>Opposite sides are equal and parallel (B)</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 (C)</p> Signup and view all the answers

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

<p>Compass (B)</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 (B)</p> Signup and view all the answers

What is the key property of congruent shapes?

<p>Corresponding sides and angles are equal (B)</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 (D)</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 (C)</p> Signup and view all the answers

What is the result of translating a shape?

<p>A shape with a different size and orientation (B)</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 (A)</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 (B)</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 (C)</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 (D)</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 (C)</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 (B)</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 (A)</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 (A)</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 (D)</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 (A)</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 (B)</p> Signup and view all the answers

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

<p>Any of the above (D)</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 (D)</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 (A)</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 (D)</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. (A)</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. (C)</p> Signup and view all the answers

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

<p>4 (C)</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 (D)</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 (A)</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 (B)</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. (C)</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. (A)</p> Signup and view all the answers

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

<p>6 (B)</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. (D)</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 (B)</p> Signup and view all the answers

What is the formula for vertically opposite angles?

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

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

<p>4 (D)</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 (C)</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. (B)</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. (B)</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 (D)</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. (C)</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. (A)</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°. (B)</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. (C)</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. (D)</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. (A)</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. (C)</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. (B)</p> Signup and view all the answers

What is the advantage of using equivalent equations?

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

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

<p>3 (A)</p> Signup and view all the answers

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

<p>Parallelogram (C)</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 (A)</p> Signup and view all the answers

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

<p>Compass (B)</p> Signup and view all the answers

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

<p>Bisecting (B)</p> Signup and view all the answers

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

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

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

<p>Perpendicular bisector (A)</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 (D)</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 (A)</p> Signup and view all the answers

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

<p>Construction (C)</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 (B)</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 (B)</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 (A)</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 (D)</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 (A)</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 (D)</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. (A)</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 (B)</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. (D)</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 (C)</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. (B)</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. (A)</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 (C)</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. (A)</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 (D)</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. (C)</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. (A)</p> Signup and view all the answers

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

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

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

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

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

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

If two angles are supplementary, what is their sum?

<p>180° (A)</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° (D)</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 (A)</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 (C)</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 (C)</p> Signup and view all the answers

What is the key concept in solving equations by inspection?

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

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

<p>Compass (C)</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 (D)</p> Signup and view all the answers

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

<p>Segment (A)</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 (B)</p> Signup and view all the answers

What is the key to identifying similar shapes?

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

What is the purpose of constructing perpendicular and parallel lines?

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

What is the characteristic of a regular polygon?

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

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

<p>Using a compass (D)</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 (B)</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 (D)</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° (D)</p> Signup and view all the answers

What type of triangle has all sides and angles equal?

<p>Equilateral triangle (C)</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 (A)</p> Signup and view all the answers

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

<p>Square (A)</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 (D)</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 (A)</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 (D)</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 (C)</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 (C)</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 (C)</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 (A)</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 (A)</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 (B)</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 (C)</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 (C)</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 (B)</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 (D)</p> Signup and view all the answers

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

<p>Rhombus (D)</p> Signup and view all the answers

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

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

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

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

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

<p>3 (A)</p> Signup and view all the answers

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

<p>All sides of equal length (B)</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 (C)</p> Signup and view all the answers

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

<p>Trapezium (C)</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 (C)</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 (B)</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 (B)</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 (A)</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 (B)</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 (D)</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 (B)</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 (C)</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 (A)</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 (B)</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 (A)</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 (A)</p> Signup and view all the answers

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