Geometry: Shapes - Rectangles, Triangles and Polygons

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Questions and Answers

Match the following terms with the shapes they do not describe:

Square = Polygon Rectangle = Square Parallelogram = Trapezoid Rhombus = Rectangle

Match each quadrilateral with the additional property that makes it a rhombus:

Parallelogram = Four equal sides Rectangle = Diagonals bisect angles Trapezoid = Two pairs of parallel sides Kite = Four equal sides

Match each type of triangle with the property it must have:

Equilateral = Three equal sides Isosceles = At least two equal sides Scalene = No equal sides Right = One 90-degree angle

Match each condition with the reason why a figure is not a rhombus:

<p>Unequal angles = Rhombuses have opposite equal angles No right angles = Rhombuses don't need to have right angles Unequal sides = Rhombuses have four equal sides Does not have parallel sides = Rhombuses are parallelograms therefore must have parallel sides</p>
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Match the side lengths to create a valid Isosceles right triangle given side 'a' and 'b' are equal:

<p>a = 7, b = 7 = c = $7\sqrt{2}$ a = 4, b = 4 = c = $4\sqrt{2}$ a = 9, b = 9 = c = $9\sqrt{2}$ a = 13, b = 13 = c = $13\sqrt{2}$</p>
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Match the pairs of quadrilaterals that always have all sides congruent:

<p>Square = Rhombus Rectangle = Kite Parallelogram = Trapezoid Isosceles Trapezoid = Rectangle</p>
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Match each shape to the reason why they are not polygons:

<p>Circle = Curved sides Oval = Curved sides Semi-circle = Curved side Any shape with opening = Polygons must be closed</p>
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Match the term to the shape it should not describe:

<p>Parallelogram = Triangle Rhombus = Trapezoid Rectangle = Rhombus Trapezoid = Square</p>
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Match each shape to the type of shape it could be categorized as:

<p>Quadrilateral = Trapezoid Pentagon = Heptagon Hexagon = Octagon Triangle = Decagon</p>
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Match each statement to the reason why it best explains why a square is a rectangle:

<p>Quadrilateral with four right angles = Rectangles must have four right angles Similar to a rectangle = Definition is not precise enough Is a rhombus = Squares are always rectangles but rectangles are not always squares Is a parallelogram = Squares meet the criteria of a parallelogram with 4 right angles</p>
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Match each term with its definition:

<p>Parallelogram = Quadrilateral with two pairs of parallel sides Rectangle = Parallelogram with four right angles Rhombus = Parallelogram with four equal sides Square = Rectangle with four equal sides</p>
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Match each additional property with the shape that it describes:

<p>Diagonals are congruent = Rectangle Diagonals are perpendicular = Rhombus Diagonals bisect each other = Parallelogram Diagonals are both perpendicular and congruent = Square</p>
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Match the sum of the angles inside of each of the following shapes:

<p>Triangle = $180^\circ$ Quadrilateral = $360^\circ$ Pentagon = $540^\circ$ Hexagon = $720^\circ$</p>
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Match each property only to the shapes that always have it:

<p>Congruent diagonals = Square and Rectangle Perpendicular diagonals = Square and Rhombus Two pairs of parallel sides = Square, Rectangle, and Rhombus Four congruent sides = Square and Rhombus</p>
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Match the requirements for a shape to be classified as regular:

<p>Triangle = Equilateral, all sides congruent Quadrilateral = Square, all sides congruent and all angles equal Pentagon = All sides congruent and all angles equal Hexagon = All sides congruent and all angles equal</p>
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Match each shape with its most specific classification:

<p>A Quadrilateral = Parallelogram A Parallelogram = Rectangle A Rectangle = Square A Rhombus = Square</p>
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Match each combination of requirements to the correct shape(s):

<p>Must be a parallelogram with all four sides congruent = Rhombus Must be a parallelogram with four right angles = Rectangle Must have one set of parallel sides = Trapezoid Must have 3 sides = Triangle</p>
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Match each figure with its respective area equation:

<p>Parallelogram = $A = b \cdot h$ Rectangle = $A = l \cdot w$ Triangle = $A = \frac{1}{2} \cdot b \cdot h$ Trapezoid = $A = \frac{1}{2} \cdot (b_1 + b_2) \cdot h$</p>
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Match each angle type with its constraint:

<p>Acute = $&gt; 0^\circ &lt; x &lt; 90^\circ$ Right = $x = 90^\circ$ Obtuse = $90^\circ &lt; x &lt; 180^\circ$ Straight = $x = 180^\circ$</p>
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Match each triangle inequality constraint with its meaning:

<p>a + b &gt; c = Two sides must be longer than the third a + c &gt; b = Two sides must be longer than the third b + c &gt; a = Two sides must be longer than the third Must follow all constraints = To be a valid triangle</p>
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Flashcards

What is a polygon?

A polygon is a closed 2D shape with straight sides.

What is a quadrilateral?

A quadrilateral is a four-sided polygon.

What is a parallelogram?

A parallelogram is a quadrilateral with opposite sides parallel and equal.

What is a rhombus?

A rhombus is a parallelogram with all four sides equal in length.

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What is an equilateral triangle?

An equilateral triangle has all three sides equal in length and all three angles equal to 60 degrees.

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What is an isosceles triangle?

An isosceles triangle has two sides of equal length.

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What is an Isosceles Right Triangle?

Right triangle with two equal sides.

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What is a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides.

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What is a rectangle?

A rectangle is a quadrilateral with four right angles.

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What is a square?

A square is a quadrilateral with four right angles and four equal sides.

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Study Notes

  • Study notes relating to questions on rectangles, parallelograms, rhombus, equilateral triangles, isosceles triangles, right triangles, quadrilaterals, polygons, trapezoids and squares

Question 1

  • The answer is square, as not all rectangles are squares

Question 2

  • The answer is square, as a square is both a parallelogram and a rhombus

Question 3

  • The answer is II, as it shows an equilateral triangle

Question 4

  • The answer is C, as a rhombus has four sides of equal length

Question 5

  • The answer is C, as it shows a triangle that is both isosceles and a right triangle

Question 6

  • The answer is A, as both squares and rhombus have all sides congruent and are quadrilaterals

Question 7

  • The answer is C, as it is a polygon

Question 8

  • The answer is D, as a square is not a trapezoid

Question 9

  • The answer is A, as a quadrilateral could also be a trapezoid

Question 10

  • The answer is A, as a square is a quadrilateral with four right angles and shares all the defining properties of a rectangle

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