Geometry Quizzes: Test Your Knowledge of Shapes and Measurements

Question 1

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the volume of the prism?

Accepted Answer

30 cm³

Answer

15 cm³

Answer

60 cm³

Answer

120 cm³

Question 2

Two similar triangles have a similarity ratio of 2:3. If the perimeter of the smaller triangle is 15 cm, what is the perimeter of the larger triangle?

Accepted Answer

22.5 cm

Answer

30 cm

Answer

10 cm

Question 3

To prove that the sum of the interior angles of a quadrilateral is 360 degrees, which method should you use?

Accepted Answer

Divide the quadrilateral into two triangles and apply the property that the sum of the interior angles of a triangle is 180 degrees.

Answer

Apply the property that the sum of the exterior angles of a quadrilateral is 360 degrees.

Answer

Apply the property that opposite angles in a parallelogram are equal.

Question 4

Calculate the area of a parallelogram with a base of 6 centimeters and a height of 4 centimeters.

Accepted Answer

24 square centimeters

Answer

10 square centimeters

Answer

12 square centimeters

Question 5

Classify the polygon as regular or irregular: A polygon with 7 equal sides and 7 equal angles.

Accepted Answer

Regular polygon

Answer

Irregular polygon

Answer

Cannot be determined

Question 6

When a two-dimensional (2D) shape is rotated around an axis perpendicular to its plane, what happens to its number of dimensions?

Accepted Answer

It stays two-dimensional.

Answer

It becomes three-dimensional.

Answer

It becomes one-dimensional.

Answer

It loses all dimensions.

Question 7

Imagine slicing a cube with a perfectly flat cut so that one half is a mirror image of the other. How many different ways can you slice the cube to get this result?

Accepted Answer

6

Answer

3

Answer

9

Question 8

A tree casts a shadow that is 20 meters long. At the same time, a pole 2 meters tall casts a shadow that is 3 meters long. Using the Pythagorean theorem, what is the height of the tree?

Accepted Answer

19.77 meters

Answer

12 meters

Answer

20 meters

Answer

15 meters

Question 9

Determine the measure of each interior angle in a regular octagon.

Accepted Answer

135°

Answer

45°

Answer

180°

Answer

90°

Question 10

Which characteristic does NOT belong to a parallelogram?

Accepted Answer

Diagonals intersect at the midpoint

Answer

Opposite sides are parallel

Answer

Opposite sides are congruent

Answer

Opposite angles are congruent

Question 11

What is the measure of each interior angle of a regular hexagon?

Accepted Answer

120 degrees

Answer

90 degrees

Answer

150 degrees

Answer

180 degrees

Question 12

Which transformation involves moving a figure without changing its size or shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 13

What is the volume of a rectangular prism with a length of 5 centimeters, a width of 3 centimeters, and a height of 2 centimeters?

Accepted Answer

30 cubic centimeters

Answer

15 cubic centimeters

Answer

60 cubic centimeters

Answer

120 cubic centimeters

Question 14

Which of the following is an example of a three-dimensional figure?

Accepted Answer

Cube

Answer

Circle

Answer

Triangle

Answer

Line segment

Question 15

What is the scale factor of a dilation that makes a figure three times larger?

Accepted Answer

3

Answer

1/3

Answer

9

Answer

27

Question 16

What is the formula for the area of a rectangle?

Accepted Answer

length x width

Answer

length + width

Answer

2(length + width)

Answer

length / width

Question 17

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

Accepted Answer

180 degrees

Answer

120 degrees

Answer

240 degrees

Answer

360 degrees

Question 18

A solid figure has two parallel circular bases connected by a curved surface. What is the name of this solid figure?

Accepted Answer

Cylinder

Answer

Cone

Answer

Sphere

Answer

Pyramid

Question 19

What is the area of a circle with a radius of 5 cm?

Accepted Answer

25π cm²

Answer

10π cm²

Answer

50π cm²

Answer

100π cm²

Question 20

What is the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a² + b² = c

Answer

a² - b² = c

Question 21

Find the surface area of a sphere with a radius of 4 centimeters.

Accepted Answer

32π cm²

Answer

16π cm²

Answer

64π cm²

Answer

128π cm²

Question 22

Which of the following is not a regular polygon?

Accepted Answer

Rectangle

Answer

Square

Answer

Hexagon

Answer

Octagon

Question 23

Identify the property that does NOT apply to a parallelogram:

Accepted Answer

All sides are congruent.

Answer

Opposite sides are parallel.

Answer

Opposite angles are equal.

Answer

Diagonals bisect each other.

Question 24

Which transformation preserves both the shape and size of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 25

Determine the perimeter of a square with a side length of 4 centimeters.

Accepted Answer

16 centimeters

Answer

8 centimeters

Answer

12 centimeters

Answer

24 centimeters

Question 26

State the Pythagorean Theorem.

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a² + c² = b²

Answer

a² - c² = b²

Question 27

Find the area of a rectangle with a length of 5 cm and a width of 3 cm.

Accepted Answer

15 cm²

Answer

8 cm²

Answer

20 cm²

Answer

35 cm²

Question 28

Which transformation changes the shape of a figure?

Accepted Answer

Stretching

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 29

Which net can form a triangular prism when folded?

Accepted Answer

Rectangle with two triangles attached to one side

Answer

Square with two triangles attached to opposite sides

Answer

Hexagon with two equilateral triangles attached to opposite sides

Answer

Circle with two triangles attached to the same side

Question 30

State the Pythagorean theorem.

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

c² = a² + b²

Question 31

Which transformation does NOT preserve the shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 32

What is the angle formed by the intersection of two perpendicular lines?

Accepted Answer

90 degrees

Answer

30 degrees

Answer

45 degrees

Answer

180 degrees

Question 33

Which 3D shape has a circular base and a single vertex?

Accepted Answer

Cone

Answer

Cylinder

Answer

Sphere

Answer

Pyramid

Question 34

Which theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?

Accepted Answer

Pythagorean theorem

Answer

Triangle theorem

Answer

Angle theorem

Answer

Perimeter theorem

Question 35

What is the volume of a cube with an edge length of 3 cm?

Accepted Answer

27 cm³

Answer

3 cm³

Answer

9 cm³

Answer

81 cm³

Question 36

Which property is NOT true for all quadrilaterals?

Accepted Answer

All sides are congruent

Answer

Opposite sides are parallel

Answer

Opposite angles are supplementary

Answer

Diagonals intersect at right angles

Question 37

Which transformation will NOT produce a congruent shape?

Accepted Answer

Scaling

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 38

Which shape is three-dimensional?

Accepted Answer

Sphere

Answer

Square

Answer

Circle

Answer

Triangle

Question 39

Which property describes a circle?

Accepted Answer

All points are the same distance from the center

Answer

Has two parallel lines tangent to it

Answer

Has four right angles

Answer

Has four congruent sides

Question 40

What is the angle formed when two perpendicular lines intersect?

Accepted Answer

90°

Answer

30°

Answer

45°

Answer

120°

Question 41

Which transformation moves a figure without changing its shape or size?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 42

What is the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

a + b = c

Question 43

Calculate the volume of a cube with a side length of 5 cm.

Accepted Answer

125 cm³

Answer

25 cm³

Answer

50 cm³

Answer

250 cm³

Question 44

Which transformation preserves angles and ratios of corresponding sides?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 45

Calculate the volume of a rectangular prism with a length of 10 centimeters, a width of 5 centimeters, and a height of 3 centimeters.

Accepted Answer

150 cubic centimeters

Answer

50 cubic centimeters

Answer

250 cubic centimeters

Answer

100 cubic centimeters

Question 46

Calculate the volume of a cone with a height of 10 centimeters and a radius of 5 centimeters. Express your answer in terms of π.

Accepted Answer

25π cm³

Answer

50π cm³

Answer

125π cm³

Question 47

To prove that the diagonals of a rhombus bisect each other perpendicularly, which of the following methods can be used?

Accepted Answer

Draw the diagonals and demonstrate that they form four congruent right triangles.

Answer

Apply the Pythagorean Theorem to establish that the diagonals are perpendicular.

Answer

Utilize the property that the diagonals of a rhombus are perpendicular to prove that they bisect each other.

Answer

The diagonals of a rhombus cannot bisect each other perpendicularly.

Question 48

Which of the following is a defining property of a square?

Accepted Answer

All sides are equal and all angles are right angles

Answer

All sides are equal, but only two angles are right angles

Answer

All angles are right angles, but only two sides are equal

Question 49

Identify the image that shows a net of a cube.

Accepted Answer

[Image of a net of a cube]

Answer

[Image of a net of a sphere]

Answer

[Image of a net of a pyramid]

Answer

[Image of a net of a triangular prism]

Question 50

Which of the following is a key characteristic of similar triangles?

Accepted Answer

Corresponding angles are congruent and corresponding sides are proportional

Answer

Corresponding sides are proportional, but corresponding angles are not congruent

Answer

Corresponding angles are congruent, but corresponding sides are not proportional

Question 51

State the Pythagorean Theorem.

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

b² - a² = c²

Answer

c² - a² = b²

Question 52

Define a regular polygon.

Accepted Answer

A polygon with all sides and angles equal

Answer

A polygon with neither all sides nor all angles equal

Answer

A polygon with all angles but not all sides equal

Answer

A polygon with all sides but not all angles equal

Question 53

Which theorem states that the sum of the interior angles of a triangle is 180 degrees?

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Law of Cosines

Answer

Theorem of Thales

Question 54

Which of the following accurately describes a cone?

Accepted Answer

Circular base and a single vertex

Answer

Rectangular base and a triangular vertex.

Answer

Two parallel circular bases

Answer

Square base and a circular vertex

Question 55

Which of the following transformations does NOT change the shape of a figure?

Accepted Answer

Translation

Answer

Dilation

Answer

Reflection

Answer

Rotation

Question 56

What is the area of a circle with a radius of 7 cm?

Accepted Answer

49π cm²

Answer

28π cm²

Answer

14π cm²

Answer

98π cm²

Question 57

Which equation represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

b² - a² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Question 58

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

Accepted Answer

It has flat faces

Answer

It is a three-dimensional shape

Answer

Every point on the surface is equidistant from the center

Question 59

What is the surface area of a cube with a side length of 5 cm?

Accepted Answer

150 cm²

Answer

75 cm²

Answer

30 cm²

Question 60

Which type of triangle has three congruent sides?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 61

What is the angle measure that, when added to a 30-degree angle, results in a right angle of 90 degrees?

Accepted Answer

60 degrees

Answer

45 degrees

Answer

120 degrees

Answer

75 degrees

Question 62

Which of the following three-dimensional shapes has a circular base and curved sides?

Accepted Answer

Cylinder

Answer

Pyramid

Answer

Cube

Answer

Sphere

Question 63

What is the primary purpose of the Pythagorean theorem?

Accepted Answer

To find the length of the missing side of a right triangle.

Answer

To calculate the area of a circle.

Answer

To determine the volume of a sphere.

Answer

To measure the angles of a quadrilateral.

Question 64

Which type of angle is greater than 90 degrees but less than 180 degrees?

Accepted Answer

Obtuse

Answer

Right

Answer

Acute

Answer

Reflex