Geometry Quizzes: Master Shapes and Spaces

Question 1

Find the sum of the interior angles of a polygon with 'n' sides.

Accepted Answer

n(n-2)°

Answer

n(n+2)°

Answer

n(2n+2)°

Answer

n(n-4)°

Question 2

Triangle PQR is reflected across the x-axis. If the original coordinates of Triangle PQR are P(2, 3), Q(6, 3), and R(4, 6), what are the coordinates of the reflected image?

Accepted Answer

P'(2, -3), Q'(6, -3), R'(4, -6)

Answer

P'(-2, 3), Q'(-6, 3), R'(-4, 6)

Answer

P'(2, 3), Q'(6, 3), R'(-4, 6)

Answer

P'(-2, -3), Q'(-6, -3), R'(-4, -6)

Question 3

In a right triangle, the hypotenuse measures 10 cm and one leg is 6 cm long. Use the Pythagorean Theorem to find the length of the other leg.

Accepted Answer

8 cm

Answer

2 cm

Answer

10 cm

Question 4

Which three-dimensional shape has 8 flat surfaces, 6 corners, and 12 straight sides?

Accepted Answer

Cube

Answer

Triangular prism

Answer

Sphere

Answer

Cylinder

Question 5

When a plane cuts through a cube parallel to one of its faces, what shape does the cross-section form?

Accepted Answer

Square

Answer

Triangle

Answer

Circle

Question 6

A parallelogram has a base of 10 cm and a height of 8 cm. Find the length of the diagonal that is not parallel to the base.

Accepted Answer

12.8 cm

Answer

6 cm

Answer

8 cm

Answer

10 cm

Question 7

What is the measure of an angle that is a straight line?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

120 degrees

Answer

270 degrees

Question 8

Which transformation involves moving a figure from one point to another without changing its shape or size?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Enlargement

Question 9

In a circle, the line segment connecting the center to a point on the circumference is called a...

Accepted Answer

Radius

Answer

Diameter

Answer

Chord

Answer

Secant

Question 10

Which of the following is NOT a type of symmetry?

Accepted Answer

Asymmetry

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 11

A figure has rotational symmetry if it...

Accepted Answer

Can be rotated a full turn and still look exactly the same

Answer

Can be rotated a half turn and still look exactly the same

Answer

Can be rotated a quarter turn and still look exactly the same

Answer

Cannot be rotated and still look exactly the same

Question 12

Which of the following solids is a three-dimensional shape with a circular base and a conical top?

Accepted Answer

Cone

Answer

Cylinder

Answer

Sphere

Answer

Pyramid

Question 13

What is the measure of an angle that complements a 45-degree angle?

Accepted Answer

90 degrees

Answer

22.5 degrees

Answer

45 degrees

Answer

67.5 degrees

Question 14

What is the formula for the area of a triangle?

Accepted Answer

A = 1/2 * base * height

Answer

A = 1/4 * base * height

Answer

A = base * height

Answer

A = 2 * base * height

Question 15

Which of the following is the equation of the line with a y-intercept of -1 and a slope of 2?

Accepted Answer

y = 2x - 1

Answer

y = -2x + 1

Answer

y = x - 2

Answer

y = -x + 2

Question 16

Which of the following is NOT a trigonometric ratio?

Accepted Answer

Perimeter

Answer

Sine

Answer

Tangent

Answer

Cosine

Question 17

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 18

Which transformation involves moving a figure from one place to another without changing its shape or size?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 19

What is the formula for the area of a circle with radius 'r'?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = 4πr²

Answer

A = πr

Question 20

What is the name of the point where the altitudes of a triangle intersect?

Accepted Answer

Orthocenter

Answer

Incenter

Answer

Circumcenter

Answer

Centroid

Question 21

Classify the triangle with angle measures of 30°, 60°, and 90°.

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Question 22

Which transformation consistently produces a similar shape regardless of the original figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 23

Determine the distance between the points (2, 3) and (-1, 5).

Accepted Answer

√13

Answer

2

Answer

5

Answer

√10

Question 24

Find the slope of a line perpendicular to y = 2x + 1.

Accepted Answer

-1/2

Answer

0

Answer

1/2

Answer

2

Question 25

Calculate the volume of a cube with a side length of 4 cm.

Accepted Answer

64 cm³

Answer

8 cm³

Answer

16 cm³

Answer

256 cm³

Question 26

Which set of numbers represents a Pythagorean triple?

Accepted Answer

(3, 4, 5)

Answer

(4, 5, 6)

Answer

(5, 6, 7)

Answer

(6, 7, 8)

Question 27

Which of the following is not a characteristic of a parallelogram?

Accepted Answer

Opposite angles are complementary.

Answer

Opposite sides are parallel.

Answer

Opposite sides are congruent.

Answer

Diagonals bisect each other.

Question 28

Which of the following transformations does not preserve the orientation of a figure?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 29

Which property is NOT true about a parallelogram?

Accepted Answer

Consecutive angles are supplementary.

Answer

Opposite sides are parallel.

Answer

Opposite sides are congruent.

Answer

Diagonals bisect each other.

Question 30

A triangle with two congruent sides is classified as a/an:

Accepted Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Right triangle

Question 31

Which transformation changes the size of a figure but not its shape?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Answer

Reflection

Question 32

Which theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse?

Accepted Answer

Pythagorean Theorem

Answer

Triangle Sum Postulate

Answer

Side-Angle-Side Postulate

Answer

Angle-Side-Angle Postulate

Question 33

Which theorem states that the exterior angles of a polygon form a straight line?

Accepted Answer

Polygon Exterior Angle Sum Theorem

Answer

Polygon Interior Angle Sum Theorem

Answer

Triangle Sum Postulate

Answer

Pythagorean Theorem

Question 34

What is the total measure of the interior angles of a quadrilateral?

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

540 degrees

Question 35

Determine the formula for calculating the area of a trapezoid:

Accepted Answer

A = (b1 + b2) * h / 2

Answer

A = l * w

Answer

A = pi * r^2

Answer

A = (s^2 * sqrt(3)) / 4

Question 36

Name the theorem that states the relationship between the side lengths of a right triangle:

Accepted Answer

Pythagorean Theorem

Answer

Euclidean Theorem

Answer

Archimedes' Theorem

Answer

Descartes' Theorem

Question 37

In a triangle, the sum of angles B and C is 120°. If angle B is 50°, what is the measure of angle C?

Accepted Answer

60°

Answer

40°

Answer

50°

Answer

70°

Question 38

Find the area of a circle with a radius of 5 centimeters.

Accepted Answer

25π cm²

Answer

50π cm²

Answer

75π cm²

Answer

100π cm²

Question 39

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

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 40

State the Pythagorean theorem.

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a + b = c

Answer

a - b = c

Question 41

Which of the following is a polygon?

Accepted Answer

Triangle

Answer

Circle

Answer

Sphere

Answer

Cone

Question 42

Which angle measurement represents a right angle?

Accepted Answer

90°

Answer

30°

Answer

45°

Answer

120°

Question 43

Write the equation of a line with a slope of 2 and a y-intercept of 3.

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

y = 2x - 3

Answer

y = 3x - 2

Question 44

In a right triangle, the side adjacent to the right angle is referred to as the:

Accepted Answer

Leg

Answer

Hypotenuse

Answer

Base

Answer

Altitude

Question 45

Which of the following constitutes a valid inductive proof technique?

Accepted Answer

Assuming a statement holds for n = k and proving it for n = k + 1

Answer

Proving a statement for n = 1, 2, and 3

Answer

Using a calculator to evaluate the statement for a large number of n

Answer

Conducting an experiment and observing the results for different values of n

Question 46

The volume of a rectangular prism with dimensions 5 cm x 3 cm x 2 cm is:

Accepted Answer

30 cm³

Answer

10 cm³

Answer

15 cm³

Answer

60 cm³

Question 47

Which postulate states that two angles that form a straight line are supplementary?

Accepted Answer

Linear Pair Postulate

Answer

Angle Addition Postulate

Answer

Vertical Angles Theorem

Answer

Triangle Sum Theorem

Question 48

What is the perimeter of a square with a side length of 4 inches?

Accepted Answer

16 inches

Answer

4 inches

Answer

8 inches

Answer

32 inches

Question 49

Which of the following is a proof technique that involves assuming the opposite of what is to be proven?

Accepted Answer

Indirect proof

Answer

Direct proof

Answer

Algebraic proof

Answer

Geometric proof

Question 50

What is the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

c² + b² = a²

Question 51

Which of the following is not a property of a rectangle?

Accepted Answer

Consecutive sides are perpendicular

Answer

Four right angles

Answer

Opposite sides are parallel

Answer

Opposite sides are congruent

Question 52

Find the volume of a sphere with a radius of 5 cm.

Accepted Answer

(4/3)100π cm³

Answer

100π cm³

Answer

500π cm³

Answer

125π cm³

Question 53

Which transformation involves a change in position without changing shape or size?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 54

If a triangle has side lengths of 3 cm, 4 cm, and 5 cm, which theorem can be used to show that it is a right triangle?

Accepted Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Angle Sum Theorem

Answer

Midsegment Theorem

Question 55

What is the equation of a circle with center (-2, 5) and radius 3?

Accepted Answer

(x + 2)² + (y - 5)² = 9

Answer

(x - 2)² + (y + 5)² = 9

Answer

(x + 5)² + (y - 2)² = 3

Answer

(x - 5)² + (y + 2)² = 3

Question 56

Find the length of the hypotenuse of a right triangle with legs of length 3 cm and 4 cm.

Accepted Answer

7 cm

Answer

5 cm

Answer

9 cm

Answer

11 cm

Question 57

Find the equation of a line with a slope of 2 that passes through point (3, 5).

Accepted Answer

y = 2x - 1

Answer

y = 1 / 2x + 4

Answer

y = -2x + 11

Answer

y = x + 6

Question 58

Which of the following methods is considered a valid geometric proof?

Accepted Answer

Proof by contradiction

Answer

Proof by authority

Answer

Proof by example

Answer

Proof by intuition

Question 59

Which of the following is NOT always true for a parallelogram?

Accepted Answer

All sides are congruent

Answer

Diagonals bisect each other

Answer

Opposite angles are equal in measure

Answer

Opposite sides are equal in length

Question 60

Which transformation will always map a figure onto itself?

Accepted Answer

Rotation of 360 degrees

Answer

Reflection

Answer

Translation

Answer

Dilation with a scale factor of 2

Question 61

Which postulate states that the angles inside a triangle add up to 180 degrees?

Accepted Answer

Triangle Sum Theorem

Answer

Exterior Angle Theorem

Answer

Pythagorean Theorem

Answer

Angle Bisector Theorem

Question 62

The Pythagorean Theorem is used to calculate what?

Accepted Answer

The length of the hypotenuse in a right triangle

Answer

The volume of a right triangle

Answer

The perimeter of a right triangle

Answer

The area of a right triangle

Question 63

Which of the following transformations preserves shape and size?

Accepted Answer

Translation

Answer

Dilation

Answer

Reflection

Answer

Rotation

Question 64

Two lines are described as perpendicular if they intersect at a 90-degree angle. Which of the following conditions ensures that two lines are perpendicular?

Accepted Answer

Their slopes are negative reciprocals of each other.

Answer

Their y-intercepts are equal.

Answer

Their slopes are zero.

Answer

Their slopes are equal.