Geometry for Ninth Graders: Master Shapes and Properties

Question 1

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

Accepted Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Question 2

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

Accepted Answer

Exactly 180 degrees

Answer

Less than 180 degrees

Answer

More than 180 degrees

Answer

Dependent on the side lengths

Question 3

In a circle, the ratio of the circumference to the diameter is known as:

Accepted Answer

A. pi

Answer

B. e

Answer

C. phi

Answer

D. tau

Question 4

What condition determines if two triangles are similar?

Accepted Answer

Same shape and proportional side lengths

Answer

Equal side lengths but different angles

Answer

Different shapes but equal side lengths

Answer

Equal angles but different side lengths

Question 5

What is a defining characteristic of all regular polygons?

Accepted Answer

Equal side lengths and equal angles

Answer

Equal side lengths but not equal angles

Answer

Equal angles but not equal side lengths

Answer

Neither equal side lengths nor equal angles

Question 6

Which of the following is the definition of a square?

Accepted Answer

A four-sided figure with four equal sides and four right angles

Answer

A four-sided figure with four equal sides and two right angles

Answer

A four-sided figure with four unequal sides and four right angles

Answer

A four-sided figure with four unequal sides and two right angles

Question 7

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 8

What is the formula for the circumference of a circle?

Accepted Answer

C = 2πr

Answer

C = πr

Answer

C = πd/2

Answer

C = 2πd

Question 9

What is the formula for the area of a rectangle?

Accepted Answer

A = lw

Answer

A = ½(base + height)

Answer

A = πr²

Answer

A = 2(length + width)

Question 10

Which of the following is a property of parallel lines?

Accepted Answer

They never intersect

Answer

They intersect at a right angle

Answer

They intersect at an acute angle

Answer

They intersect at an obtuse angle

Question 11

What is the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

b² - c² = a²

Question 12

Which of the following is a three-dimensional shape?

Accepted Answer

Sphere

Answer

Square

Answer

Rectangle

Answer

Triangle

Question 13

What is the formula for the volume of a cube?

Accepted Answer

V = l³

Answer

V = 4/3πr³

Answer

V = πr²h

Answer

V = 2(lw + lh + hw)

Question 14

What theorem relates the lengths of the sides of a right triangle?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a + b = c

Answer

a/b = c

Question 15

Which shape has four equal sides and four right angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Rhombus

Question 16

Which transformation does NOT preserve the size and shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 17

Which of the following is an example of a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Kite

Question 18

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

Accepted Answer

360 degrees

Answer

180 degrees

Answer

540 degrees

Answer

720 degrees

Question 19

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

Accepted Answer

It has parallel sides

Answer

It has a constant radius

Answer

It has an infinite number of diameters

Answer

It has congruent angles throughout

Question 20

The sum of the interior angles of a triangle is:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 21

Which of the following shapes has the most sides?

Accepted Answer

Hexagon

Answer

Triangle

Answer

Quadrilateral

Answer

Pentagon

Question 22

Two angles that sum up to 90 degrees are called:

Accepted Answer

Complementary angles

Answer

Supplementary angles

Answer

Vertical angles

Answer

Adjacent angles

Question 23

Which of the following is a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Parallelogram

Question 24

The Pythagorean theorem is used to find the:

Accepted Answer

Length of the missing side of a right triangle

Answer

Area of a circle

Answer

Volume of a sphere

Answer

Perimeter of a square

Question 25

The area of a triangle with a base of 5 cm and a height of 3 cm is:

Accepted Answer

7.5 cm^2

Answer

8 cm^2

Answer

15 cm^2

Answer

3 cm^2

Question 26

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

Accepted Answer

360 degrees

Answer

180 degrees

Answer

270 degrees

Answer

540 degrees

Question 27

Which of the following transformations involves a flip over a line?

Accepted Answer

Reflection

Answer

Translation

Answer

Rotation

Answer

Dilation

Question 28

A three-dimensional figure with two parallel circular bases is called a:

Accepted Answer

Cylinder

Answer

Sphere

Answer

Cone

Answer

Pyramid

Question 29

The Pythagorean Theorem states that in a right triangle:

Accepted Answer

The sum of the squares of the two shorter sides is equal to the square of the longest side.

Answer

The sum of the angles is 180 degrees.

Answer

The area is equal to half the product of the two shorter sides.

Answer

The longest side is always opposite the largest angle.

Question 30

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

Accepted Answer

180 degrees

Answer

45 degrees

Answer

90 degrees

Answer

360 degrees

Question 31

A triangle with two equal sides is known as a(n):

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 32

Select the correct formula for calculating the area of a circle:

Accepted Answer

A = πr^2

Answer

A = 2πr

Answer

A = πr

Answer

A = 4πr

Question 33

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

Accepted Answer

360 degrees

Answer

180 degrees

Answer

540 degrees

Answer

720 degrees

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 Sum Theorem

Answer

Sine Theorem

Question 35

Which of the following is a regular polygon?

Accepted Answer

A triangle with equal sides and equal angles

Answer

A rectangle with unequal diagonals

Answer

A pentagon with five equal sides but unequal angles

Answer

A hexagon with six unequal sides and equal angles

Question 36

Which of the following accurately describes the diagonals of a square?

Accepted Answer

Perpendicular and bisect each other.

Answer

Perpendicular but do not bisect each other.

Answer

Parallel but do not bisect each other.

Answer

Neither perpendicular nor parallel.

Question 37

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

Accepted Answer

Pythagorean theorem

Answer

Trigonometric theorem

Answer

Euclidean theorem

Answer

Pascal's theorem

Question 38

Which polygon is characterized by equal side lengths and equal angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Parallelogram

Question 39

Which property does NOT apply to a rectangle?

Accepted Answer

All sides are equal in length.

Answer

Opposite sides are parallel.

Answer

All angles are right angles.

Answer

Diagonals are congruent.

Question 40

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 41

Which formula calculates the area of a circle?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = πd²

Answer

A = 4πr

Question 42

Which set of numbers is NOT a Pythagorean triple?

Accepted Answer

(10, 25, 26)

Answer

(3, 4, 5)

Answer

(5, 12, 13)

Answer

(8, 15, 17)

Question 43

Convert 60 degrees to radians.

Accepted Answer

π/6 radians

Answer

π/3 radians

Answer

π/12 radians

Answer

π/4 radians

Question 44

Which property does NOT belong to a triangle?

Accepted Answer

All three angles are equal.

Answer

The sum of the interior angles is 180 degrees.

Answer

Opposite sides are congruent.

Answer

The sum of the exterior angles is 360 degrees.

Question 45

What is the measurement of an angle that is complementary to a 30-degree angle?

Accepted Answer

90 degrees

Answer

45 degrees

Answer

60 degrees

Answer

120 degrees

Question 46

Which shape is a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Trapezoid

Answer

Parallelogram

Question 47

What is the smallest angle in a 3-4-5 right triangle?

Accepted Answer

30 degrees

Answer

45 degrees

Answer

60 degrees

Answer

90 degrees

Question 48

Which property is NOT characteristic of a circle?

Accepted Answer

Three straight sides

Answer

Fixed radius from the center

Answer

Symmetrical shape

Answer

Enclosed by a single curved line

Question 49

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 50

Which type of triangle has all three sides congruent?

Accepted Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Answer

Right

Question 51

Which formula calculates the area of a circle?

Accepted Answer

A = πr²

Answer

A = 2πr

Answer

A = πd

Answer

A = 4πr²

Question 52

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

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

a² - b² = c²

Answer

a/b = c

Question 53

Which theorem states that any point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment?

Accepted Answer

Perpendicular Bisector Theorem

Answer

Triangle Inequality Theorem

Answer

Midsegment Theorem

Answer

Angle Bisector Theorem

Question 54

Which characteristic is unique to regular polygons?

Accepted Answer

Both equal side lengths and equal interior angles

Answer

Equal side lengths

Answer

Equal interior angles

Answer

Neither equal side lengths nor equal interior angles

Question 55

Which property is NOT characteristic of a parallelogram?

Accepted Answer

Angles are always right angles.

Answer

Opposite sides are parallel and congruent.

Answer

Opposite angles are congruent.

Answer

Diagonals bisect each other.

Question 56

What is the sum of the interior angles of a triangle with a right angle?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 57

Which of the following is NOT a type of angle measure?

Accepted Answer

Circular

Answer

Acute

Answer

Obtuse

Answer

Straight

Question 58

Which equation represents the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a² + c² = b²

Answer

a² - c² = b²

Question 59

Which figure is NOT a polygon?

Accepted Answer

Circle

Answer

Triangle

Answer

Square

Answer

Pentagon

Question 60

Which property does NOT belong to a circle?

Accepted Answer

It has four sides.

Answer

It has a radius.

Answer

It has a circumference.

Answer

It has a center point.

Question 61

Which theorem relates the lengths of the sides of a right triangle?

Accepted Answer

The Pythagorean Theorem

Answer

The Triangle Inequality Theorem

Answer

The Law of Cosines

Answer

The Law of Sines

Question 62

Which type of symmetry is NOT a reflection?

Accepted Answer

Rotational symmetry

Answer

Horizontal reflection

Answer

Diagonal reflection

Answer

Vertical reflection

Question 63

Find the measure of the angle between the hour and minute hands of a clock at 9:45.

Accepted Answer

157.5°

Answer

90°

Answer

72°

Answer

120°

Question 64

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

Accepted Answer

It has four unequal sides.

Answer

It has four right angles.

Answer

It is a regular quadrilateral.

Answer

Its diagonals intersect at right angles and bisect each other.