wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Geometry Quiz

Total questions: 106

Worksheet time: 2hrs 58mins

Name
Class
Date
1.

The measure of two angles in a triangle are 60° and 85°. What is the measure of the third angle?

a)

40°

b)

80°

c)

45°

d)

60°

2.

Corresponding parts of congruent triangles are _____________.

a)

Corresponding

b)

Similar

c)

Parallel

d)

Congruent

3.

Which statement is correct?

a)

If two pairs of corresponding angles and an included side are congruent, the triangles are congruent.

b)

If any two pairs of sides and an angle are congruent, the triangles are congruent.

c)

If any pairs of sides and angles are congruent, the triangles are congruent.

d)

All triangles are congruent because they all have 180°.

4.

The measure of 2 angle of a triangle are 60° and 75°. What is the measure of the third angle?

a)

40°

b)

80°

c)

45°

d)

60°

5.

Which of the statements below provides sufficient information to guarantee that two triangles are congruent?

a)

The triangles have three pairs of congruent corresponding angles.

b)

The triangles have two pairs of congruent corresponding sides and one pair of congruent corresponding angles.

6.

Identify the missing congruent parts in the diagram:

4 lines
7.

Find the value of the variable that makes the triangles congruent.

4 lines
8.

Are these triangles congruent? Explain.

4 lines
9.

Identify the type of triangle in the given figure.

a)

Right Triangle

b)

Equilateral Triangle

c)

Isosceles Triangle

d)

Scalene Triangle

10.

In the figure below, find the missing angles measure.

a)

50∞

b)

55∞

c)

65∞

11.

The diagram shows an isosceles triangle. What is the measure of angle A?

a)

40∞

b)

50∞

c)

60∞

d)

65∞

12.

If one angle of a parallelogram is 60°, what is the measure of its consecutive angle?

a)

120°

b)

90°

c)

60°

d)

180°

13.

In a parallelogram, the diagonals always...

a)

Bisect each other

b)

Are equal in length

c)

Are perpendicular to each other

d)

Divide the parallelogram into four equal triangles

14.

Which set of side lengths cannot form a triangle according to the Triangle Inequality Theorem?

a)

6 cm, 4 cm, 8 cm

b)

5 cm, 7 cm, 12 cm

c)

6 cm, 9 cm, 14 cm

d)

9 cm, 5 cm, 5 cm

15.

An equilateral triangle has three angles of (a)   degrees each.

16.

The sum of the interior angles of any triangle is (a)   degrees.

17.

The opposite angles in a parallelogram are always (a)   .

18.

Consecutive angles of a parallelogram are always (a)   angles.

19.

A parallelogram has one side of 10 cm and another side of 6 cm. can the perimeter be 30cm? Explain.

4 lines
20.

What is the measure of the exterior angle of an equilateral triangle?

4 lines
21.

Which of the following statements is always true for a parallelogram?

a)

All angles measure 90°

b)

Opposite sides are both equal and parallel

c)

The diagonals intersect at right angles

d)

Only two sides are parallel

22.

If a four-sided figure has two pairs of opposite sides that are both equal in length and parallel, what type of shape is it?

a)

Trapezoid

b)

Rectangle

c)

Parallelogram

d)

Kite

23.

A parallelogram has one angle measuring 60°. What are the measures of the other three angles?

a)

60°,120°,60°

b)

60°,120°,120°

c)

90°,90°,90°

d)

30°,150°,30°

24.

Which statement about the diagonals of a parallelogram is correct?

a)

They are always of equal length

b)

They bisect each other at their midpoint

c)

They always form right angles

d)

They do not intersect

25.

Which is the formula for calculating the slope of a line passing through two points (x1,y1) (x2,y2)?

4 lines
26.

If two lines have the same slope then, the lines are:

a)

Perpendicular

b)

Parallel

c)

Intersecting at 90°

d)

Coinciding

27.

Which is the slope of a line that passes through the points (4,2) and (9,6)?

a)

1/5

b)

1/2

c)

1/3

d)

5/4

28.

Match each quadrilateral to one of its characteristics. Write the number next to each quadrilateral's corresponding property. Match each property to only on quadrilateral.

4 lines
29.

Line l is ‖ to line M if the slope of line l is 7/5 the slope for line M must be __________.

4 lines
30.

The slope of a horizontal line is always ________.

4 lines
31.

A student asserts that while squares are rectangles, Rectangles can not be squares. Discuss why this statement holds true based on the properties of these quadrilaterals.

4 lines
32.

Draw a line parallel to the line below then complete the statement below. The slope of the line is ___________________.

4 lines
33.

If cos(30°) = , what is sin(60°)?

a)

1

b)

1/2

c)

√3/2

d)

√2/2

34.

Which of the following equations correctly represents the sine ratio for angle A in a right triangle?

a)

sin A = adjacent/hypotenuse

b)

sin A = opposite/hypotenuse

c)

sin A = hypotenuse/opposite

d)

sin A = adjacent/opposite

35.

What is the definition of the tangent ratio in a right triangle?

a)

Adjacent / Hypotenuse

b)

Opposite / Hypotenuse

c)

Opposite / Adjacent

d)

Hypotenuse / Opposite

36.

If, which of the following is true?

a)

The opposite side is equal to the hypotenuse.

b)

The opposite side is equal to the adjacent side.

c)

The adjacent side is equal to the hypotenuse.

d)

The opposite side is twice the adjacent side.

37.

Which equation correctly represents the tangent ratio for angle A in a right triangle?

a)

tan A = opposite/adjacent

b)

tan A = adjacent/opposite

c)

tan A = hypotenuse/opposite

d)

tan A = hypotenuse/adjacent

38.

The cosine of an angle in a right triangle is the ratio of the (a)   side to the hypotenuse.

39.

The tangent of an angle in a right triangle is the ratio of the (a)   side to the adjacent side.

40.

Match each trigonometric value to its correct angle measure:

4 lines
41.

A ladder leans against a wall forming a 65° angle with the ground. If the ladder is 12 feet long, how high does it reach on the wall? Show your calculations using the cosine ratio.

4 lines
42.

A ramp rises to a height of 2.5 meters over a horizontal distance of 6 meters. Find the angle of elevation using the tangent ratio. Show your calculations.

4 lines
43.

The measure of 2 angles of a triangle are 60° and 85°. What is the measure of the third angle?

a)

40°

b)

80°

c)

45°

d)

60°

44.

Complete the statement below. Corresponding parts of congruent triangles are ________________.

a)

Corresponding

b)

Similar

c)

Parallel

d)

Congruent

45.

Which of these statements is correct?

a)

If any 2 pairs of sides and angle are congruent then the triangles are congruent.

b)

If any 2 pairs of corresponding angles and an included side are congruent then the triangles are congruent.

c)

If any pairs of sides and angles are congruent then the triangles are congruent.

d)

All triangles are congruent because they all have 180°.

46.

Study the diagram below and complete each statement.

4 lines
47.

Determine whether the given triangles are congruent.

4 lines
48.

Find the value of the variable that results in congruent triangles.

4 lines
49.

Identify the type of triangle in the given figure.

a)

Scalene Triangle

b)

Isosceles Triangle

c)

Equilateral Triangle

d)

Right Triangle

50.

In the figure below, find the missing angles measure.

a)

50°

b)

55°

c)

65°

d)

75°

51.

Which statement about an equilateral triangle is correct?

a)

Only two sides are equal

b)

All angles measure 60°

c)

The sum of all angles is 270°

d)

It has one right angle

52.

On an equilateral triangle, If one side is 7 cm, what is the perimeter?

a)

14 cm

b)

21 cm

c)

28 cm

d)

35 cm

53.

The diagram shows an isosceles triangle. What is the measure of angle A?

a)

40°

b)

50°

c)

60°

d)

80°

54.

The remote angles to an exterior angle of a triangle are _______________________

a)

the angles adjacent to the exterior angle

b)

the angles that share the same vertex with the exterior angle

c)

the angles that are on the same line as the exterior angle

d)

the interior angles that do not share the same vertex with but sum up to the exterior.

55.

Complete each statement below. An isosceles triangle has exactly (a)   equal sides.

56.

An equilateral triangle has three angles of (a)   degrees each.

57.

The sum of the interior angles of any triangle is (a)   degrees.

58.

In an isosceles triangle, the two equal sides are called __________, and the third side is called the __________.

a)

legs

b)

base

59.

Which set of side lengths can form a triangle according to the Triangle Inequality Theorem?

a)

6 cm, 4 cm, 8 cm

b)

5 cm, 7 cm, 12 cm

c)

6 cm, 8 cm, 14 cm

d)

9 cm, 5 cm, 3 cm

60.

What does the Triangle Inequality Theorem state?

a)

The sum of two sides of a triangle must be greater than the third side.

b)

The sum of any two sides must be equal to the third side.

c)

The longest side must always be twice the shortest side.

d)

The difference between two sides must always be greater than the third side.

61.

Which of the following statements is true?

a)

A triangle can have sides measuring 2 cm, 3 cm, and 7 cm.

b)

A triangle must have all three angles equal to 90°.

c)

The sum of any two sides of a triangle must be greater than the third side.

d)

The smallest angle in a triangle is always opposite the longest side.

62.

Which of the following is always true about a parallelogram?

a)

Opposite sides are equal and parallel

b)

All angles are right angles

c)

Diagonals are perpendicular

d)

All sides are equal

63.

If one angle of a parallelogram is 120°, what is the measure of its consecutive angle?

a)

120°

b)

90°

c)

60°

d)

180°

64.

In a parallelogram, the diagonals always...

a)

Bisect each other

b)

Are equal in length

c)

Are perpendicular to each other

d)

Divide the parallelogram into four equal triangles

65.

Fill in the blank: If a triangle has sides of lengths 8 cm and 15 cm, the possible values for the third side must be between _____________________ cm and _____________________ cm.

a)

7

b)

23

66.

Fill in the blank: In any triangle, the longest side is always opposite the (a)   angle.

67.

The opposite angles in a parallelogram are always (a)   .

68.

Consecutive angles of a parallelogram are always (a)   angles.

69.

A hiking trail forms a triangle between three mountains: A, B, and C. The distances between the mountains are: Mountain A to Mountain B: 12 km Mountain B to Mountain C: 9 km What is the possible range for the distance from Mountain A to Mountain C?

a)

Between 3 km and 21 km

b)

Between 4 km and 25 km

c)

Between 1 km and 15 km

d)

Between 4 km and 20 km

70.

Which of the following is always true for a parallelogram?

a)

All angles are right angles

b)

Opposite sides are equal and parallel

c)

Diagonals are perpendicular

d)

Only one pair of sides is parallel

71.

If a quadrilateral has opposite sides that are both parallel and equal in length, what type of shape is it?

a)

Trapezoid

b)

Rhombus

c)

Parallelogram

d)

Kite

72.

Which condition is NOT sufficient to prove a quadrilateral is a parallelogram?

a)

Opposite sides are equal

b)

Opposite angles are equal

c)

One pair of opposite sides is both equal and parallel

d)

The diagonals are perpendicular

73.

A parallelogram has angles measuring 70° and 110°. What is the measure of the other two angles?

a)

70° and 110°

b)

90° and 90°

c)

80° and 100°

d)

60° and 120°

74.

Which of the following quadrilaterals is always a parallelogram?

a)

A rhombus

b)

A trapezium

c)

A kite

d)

A triangle

75.

Which of the following is true about the diagonals of a parallelogram?

a)

They are always equal in length

b)

They bisect each other

c)

They are perpendicular

d)

They never intersect

76.

Fill in the Blank: A quadrilateral is a parallelogram if one pair of opposite sides is both _________________ and _________________ .

a)

equal

b)

parallel

77.

Fill in the Blank: If the diagonals of a parallelogram are equal, then the parallelogram is a (a)   .

78.

Match the quadrilateral to one of its properties write the number next to each quadrilateral to its corresponding property: Quadrilateral Property 1 Rhombus Opposite sides are equal and all angles are 90° 2 Rectangle All sides are equal 3 Parallelogram All sides and angles are equal 4 Square Opposite sides are equal and parallel

4 lines
79.

A quadrilateral has one pair of opposite sides equal and parallel. However, its diagonals are not equal. Can we conclude that this shape is a parallelogram? Justify your answer.

4 lines
80.

A student claims that a parallelogram with equal diagonals is necessarily a square. Do you agree? Explain why or why not.

4 lines
81.

Which of the following is always true about a rectangle?

a)

All four sides are equal

b)

All four angles are right angles

c)

Diagonals are perpendicular

d)

It has only one pair of parallel sides

82.

Which of the following is a property of a rhombus but NOT necessarily a rectangle?

a)

Diagonals bisect each other

b)

Opposite sides are parallel

c)

All sides are equal in length

d)

Opposite angles are equal

83.

Which of the following conditions is true for all parallelograms?

a)

All angles are 90 degrees

b)

Opposite sides are parallel and equal

c)

All four sides are equal

d)

Diagonals are equal in length

84.

Which of the following statements about a rectangle is FALSE?

a)

Opposite sides are parallel

b)

The diagonals bisect each other

c)

The diagonals are perpendicular

d)

It has four right angles

85.

What is the formula for calculating the slope of a line passing through two points (x1,y1) (x2,y2)?

4 lines
86.

If the slopes of two lines are equal, the lines are:

a)

Perpendicular

b)

Parallel

c)

Intersecting at 90°

d)

Coinciding

87.

What is the slope of a line that passes through the points (3,2) and (7,6)?

a)

1/5

b)

1/2

c)

1/3

d)

1/1

88.

Two consecutive line segments m and l of a parallelogram have slopes 1/2 and -1/2. what are the slopes of the other two line segments of the parallelogram?

a)

1/3 and -1/5

b)

1/2 and 1/-2

c)

1/2 and 1/2

d)

-1/2 and -1/2

89.

Fill in the blank: The slope of a horizontal line is always (a)   .

90.

Two lines are parallel if they have the same (a)   .

91.

A (a)   is a parallelogram with four right angles and equal diagonals.

92.

A rhombus has diagonals that are ______________ and _______________ each other.

a)

perpendicular

b)

bisect

93.

Proof-Based Question: A student claims that all squares are rhombuses, but not all rhombuses are squares. Explain why this statement is true using properties of quadrilaterals.

4 lines
94.

What is the coordinate of the fourth vertex of the parallelogram?

4 lines
95.

What is the slope of a line perpendicular to a line with a slope of 3?

a)

3

b)

-3

c)

1/3

d)

-1/3

96.

If two lines are perpendicular, their slopes are:

a)

Equal

b)

Opposite

c)

Negative reciprocals

d)

The same as their y-intercepts

97.

Which equation represents a line perpendicular to y=2x+5?

a)

y= -1/2x+3

b)

y= 2x−1

c)

y= 1/2x+4

d)

y= −2x+7

98.

Which formula is used to find the distance between two points (x1,y1) and (x2,y2) in a coordinate plane?

4 lines
99.

What is the distance between the points A(3,4) and B(7,1)?

a)

5 units

b)

7 units

c)

6 units

d)

8 units

100.

If two segments have the same length in a coordinate proof, what can be concluded?

a)

They are perpendicular

b)

They are parallel

c)

They are congruent

d)

They bisect each other

101.

Given the points P(2,3), and Q(6,7), what is the length of segment PQ?

a)

4√2

b)

5

c)

6

d)

3√2

102.

Triangle ABC has vertices at A(1,2), B(4,6), and C(7,2). Prove whether △ABC is isosceles.

a)

Yes, because AB=BC

b)

Yes, because AC = BC.

c)

No, because all sides are different

d)

Yes, because AB = AC.

103.

Which of the following statements is true about perpendicular lines?

a)

They have the same slope

b)

Their slopes add up to zero

c)

Their slopes are negative reciprocals

d)

They never intersect

104.

Determine if the lines with equations y=−1/4x+2 and y=4x−3 are perpendicular.

a)

Yes

b)

No

c)

Cannot be determined

d)

Only if they have the same y-intercept

105.

A quadrilateral has vertices A(1,2), B(4,6), C(7,2), and D(4,-2). Prove that the diagonals of the quadrilateral are perpendicular. By finding the slopes of AC and BD.

4 lines
106.

Prove that the triangle formed by points A(−1,3), B(3,7), and C(7,3) is a right triangle. By comparing the slopes of all three segments.

4 lines