Triangles: Interactive Quizzes and Learning Activities

Question 1

Which equation represents the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

c² + b² = a²

Question 2

Which theorem relates the lengths of the sides of a triangle to the lengths of the corresponding medians?

Accepted Answer

Median Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Ceva's Theorem

Question 3

Which of these is NOT used to classify triangles based on their sides?

Accepted Answer

Obtuse

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 4

Which of these angle measurements characterizes an obtuse angle?

Accepted Answer

Greater than 90 degrees

Answer

Less than 90 degrees

Answer

Equal to 90 degrees

Answer

Equal to 180 degrees

Question 5

A triangle with all its angles measuring less than 90 degrees is classified as:

Accepted Answer

Acute

Answer

Right

Answer

Obtuse

Answer

Scalene

Question 6

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

Accepted Answer

Equal to the sum of the opposite interior angles

Answer

Equal to the difference of the opposite interior angles

Answer

Always less than 180 degrees

Answer

Always greater than 180 degrees

Question 7

Which of the following is **not** a type of triangle based on **sides**?

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 8

What is the **Pythagorean Theorem** used for?

Accepted Answer

Finding the length of the hypotenuse in a right triangle

Answer

Calculating the area of a triangle

Answer

Finding the perimeter of a triangle

Answer

Measuring the interior angles of a triangle

Question 9

What is the perimeter of a triangle with side lengths of **5 cm**, **7 cm**, and **9 cm**?

Accepted Answer

21 cm

Answer

12 cm

Answer

18 cm

Answer

27 cm

Question 10

The **area** of a triangle with a base of 5 cm and a height of 4 cm is:

Accepted Answer

10 sq cm

Answer

5 sq cm

Answer

20 sq cm

Answer

40 sq cm

Question 11

Which formula is used to find the **perimeter** of a triangle?

Accepted Answer

P = a + b + c

Answer

A = ½ * b * h

Answer

A = s^2

Answer

V = l * w * h

Question 12

The altitude of a triangle is a line segment from a vertex to:

Accepted Answer

The opposite side

Answer

The midpoint of the opposite side

Answer

The midpoint of two sides

Answer

A side parallel to the base

Question 13

Which property is NOT true for an equilateral triangle?

Accepted Answer

Opposite sides are parallel

Answer

All sides have equal length

Answer

All angles measure the same

Answer

Diagonals bisect the angles

Question 14

According to which theorem is the sum of the interior angles of any triangle equal to 180 degrees?

Accepted Answer

Angle Sum Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Hypotenuse Theorem

Question 15

What is the measure of an exterior angle of a triangle equal to?

Accepted Answer

The sum of the opposite interior angles

Answer

Half of the sum of the opposite interior angles

Answer

The difference of the opposite interior angles

Answer

Twice the opposite interior angle

Question 16

Which type of triangle has one right angle?

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Question 17

What is the primary purpose of the Pythagorean Theorem?

Accepted Answer

Calculating the length of sides in right triangles

Answer

Calculating the area of a triangle

Answer

Calculating the perimeter of a triangle

Answer

Calculating the angles of a triangle

Question 18

Which similarity criterion states that if three sides of one triangle are proportional to three sides of another triangle, then the triangles are similar?

Accepted Answer

SSS (Side-Side-Side)

Answer

SAS (Side-Angle-Side)

Answer

ASA (Angle-Side-Angle)

Answer

SSA (Side-Side-Angle)

Question 19

Calculate the height of a triangle with an area of 24 sq cm and a base length of 8 cm.

Accepted Answer

6 cm

Answer

3 cm

Answer

12 cm

Answer

24 cm

Question 20

Which of the following triangles has an angle of 90 degrees?

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 21

The sum of the exterior angles of a triangle is:

Accepted Answer

360 degrees

Answer

90 degrees

Answer

180 degrees

Answer

270 degrees

Question 22

Which of the following is a special type of triangle that has three congruent sides?

Accepted Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Answer

Right

Question 23

If the area of a triangle is 36 square units, and its base is 12 units long, what is its height?

Accepted Answer

6 units

Answer

3 units

Answer

9 units

Answer

12 units

Question 24

Which statement about triangles is NOT true?

Accepted Answer

The opposite sides are parallel.

Answer

The sum of the interior angles is 180 degrees.

Answer

The sum of the exterior angles is 360 degrees.

Answer

The sum of any two sides is always greater than the third side.

Question 25

What is the formula for calculating the area of a triangle?

Accepted Answer

A = (1/2) * base * height

Answer

A = base * height

Answer

A = π * radius^2

Answer

A = side^2

Question 26

State the Pythagorean theorem.

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

c^2 - a^2 = b^2

Answer

a^2 + c^2 = b^2

Question 27

A triangle with two equal sides is known as a:

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Right

Question 28

Which of the following formulas is used to calculate the area of a triangle?

Accepted Answer

A = 1/2 * b * h

Answer

A = b * h

Answer

A = l * w

Answer

A = πr²

Question 29

What is the Pythagorean theorem used to find?

Accepted Answer

The length of the hypotenuse of a right triangle

Answer

The area of a square

Answer

The volume of a cone

Answer

The circumference of a circle

Question 30

Which of the following is a property of all triangles?

Accepted Answer

The sum of the interior angles is 180 degrees.

Answer

Opposite sides are parallel.

Answer

All angles are equal.

Answer

The longest side is opposite the largest angle.

Question 31

In a right triangle, the side opposite the right angle is called the:

Accepted Answer

Opposite side

Answer

Hypotenuse

Answer

Adjacent side

Answer

Leg

Question 32

The perimeter of a triangle is 36 inches. If one side is 12 inches, what is the sum of the lengths of the other two sides?

Accepted Answer

24 inches

Answer

12 inches

Answer

18 inches

Answer

30 inches

Question 33

Which of the following statements about triangles is always true?

Accepted Answer

The sum of the interior angles is 180 degrees.

Answer

The area of a triangle is always greater than the area of a square with the same perimeter.

Answer

The longest side is always opposite the largest angle.

Question 34

Calculate the area of a triangle with a base of 12 cm and a height of 6 cm.

Accepted Answer

36 cm²

Answer

144 cm²

Answer

72 cm²

Answer

18 cm²

Question 35

Find the perimeter of a triangle with sides of length 4 cm, 6 cm, and 8 cm.

Accepted Answer

18 cm

Answer

12 cm

Answer

24 cm

Question 36

Which triangle has the largest area among the following options?

Accepted Answer

Triangle with base 10 cm and height 8 cm

Answer

Triangle with base 4 cm and height 3 cm

Answer

Triangle with base 6 cm and height 5 cm

Answer

Triangle with base 8 cm and height 6 cm

Question 37

Classify the triangle that has angles measuring 45°, 45°, and 90°.

Accepted Answer

Right

Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Question 38

Which mathematical equation represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

a - b = c

Answer

a² - b² = c

Question 39

Which set of side lengths cannot form a valid triangle?

Accepted Answer

5 cm, 12 cm, 18 cm

Answer

3 cm, 4 cm, 5 cm

Answer

6 cm, 8 cm, 10 cm

Question 40

Which of the following is NOT a property of all triangles?

Accepted Answer

All angles add up to 180 degrees

Answer

They have three sides

Answer

The sum of the lengths of any two sides is greater than the length of the third side

Answer

They have three angles

Question 41

A triangle with all sides of equal length is called a(n):

Accepted Answer

Equilateral triangle

Answer

Right triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Question 42

A triangle with one right angle is called a(n):

Accepted Answer

Right triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Isosceles triangle

Question 43

What is the perimeter of a triangle with sides measuring 5 cm, 7 cm, and 10 cm?

Accepted Answer

22 cm

Answer

15 cm

Answer

50 cm

Answer

35 cm

Question 44

A triangle has a base of 8 cm and a height of 6 cm. What is its area?

Accepted Answer

24 cm²

Answer

14 cm²

Answer

48 cm²

Answer

12 cm²

Question 45

Which of the following sets of angles could be the angles of a triangle?

Accepted Answer

30°, 60°, 90°

Answer

20°, 70°, 110°

Answer

10°, 20°, 150°

Answer

40°, 50°, 100°

Question 46

A triangle with two equal sides and two equal angles is called a(n):

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 47

If two angles of a triangle measure 50° and 70°, what is the measure of the third angle?

Accepted Answer

60°

Answer

100°

Answer

80°

Answer

120°

Question 48

A triangle with all three angles less than 90° is called a(n):

Accepted Answer

Acute triangle

Answer

Scalene triangle

Answer

Obtuse triangle

Answer

Right triangle

Question 49

Which of the following statements is TRUE about the sides of a triangle?

Accepted Answer

The sum of the lengths of any two sides is greater than the length of the third side

Answer

The shortest side is always opposite the smallest angle

Answer

The longest side is always opposite the largest angle

Question 50

Which of the following is NOT a characteristic of a triangle?

Accepted Answer

Four sides

Answer

Three angles

Answer

Can have three congruent sides

Answer

Closed figure

Question 51

Classify the triangle with sides measuring 5 cm, 5 cm, and 7 cm.

Accepted Answer

Isosceles

Answer

Scalene

Answer

Right

Answer

Equilateral

Question 52

What is the perimeter of a triangle with sides of length 10 cm, 12 cm, and 15 cm?

Accepted Answer

37 cm

Answer

50 cm

Answer

30 cm

Answer

42 cm

Question 53

Which of the following is the formula for calculating the area of a triangle?

Accepted Answer

1/2 * base * height

Answer

base * height

Answer

1/4 * base * height

Answer

2 * base * height

Question 54

Find the area of a triangle with a base of 8 cm and a height of 6 cm.

Accepted Answer

24 cm²

Answer

12 cm²

Answer

32 cm²

Answer

48 cm²

Question 55

Which type of triangle has three equal angles?

Accepted Answer

Equilateral

Answer

Right

Answer

Scalene

Answer

Isosceles

Question 56

Identify the right triangle from the following options:

Accepted Answer

4, 5, 6

Answer

3, 4, 5

Answer

6, 8, 10

Answer

5, 7, 8

Question 57

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

Accepted Answer

180°

Answer

360°

Answer

90°

Answer

270°

Question 58

Which of the following is NOT a property of a scalene triangle?

Accepted Answer

Has two equal sides

Answer

Has three unequal sides

Answer

Has no congruent angles

Answer

Has three unequal angles

Question 59

A triangle with sides measuring 5 cm, 12 cm, and 13 cm is classified as:

Accepted Answer

Scalene

Answer

Equilateral

Answer

Right

Answer

Isosceles