Master Triangle Properties: Online Quizzes and Practice

Question 1

In a right-angled triangle, what does the square of the hypotenuse's length equal according to Pythagoras' theorem?

Accepted Answer

The sum of the squares of the other two sides' lengths

Answer

The difference of the squares of the other two sides' lengths

Answer

The product of the squares of the other two sides' lengths

Question 2

Which property of triangles states that the sum of their interior angles is always 180 degrees?

Accepted Answer

Angle Sum Property

Answer

Exterior Angle Property

Answer

Pythagoras' Theorem

Answer

Triangle Inequality Theorem

Question 3

Which condition must be met for the Triangle Inequality Theorem to hold true?

Accepted Answer

The length of any two sides must be greater than the length of the third side.

Answer

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

Answer

The sum of any two sides must be less than the length of the third side.

Question 4

Which theorem can be used to prove that triangles with three sides of equal length are congruent?

Accepted Answer

Side-Side-Side (SSS) Congruence Theorem

Answer

Side-Angle-Side (SAS) Congruence Theorem

Answer

Angle-Side-Angle (ASA) Congruence Theorem

Answer

Angle-Angle-Side (AAS) Congruence Theorem

Question 5

Find the area of a triangle with a base of 12 cm and a height of 8 cm.

Accepted Answer

48 cm²

Answer

24 cm²

Answer

96 cm²

Answer

192 cm²

Question 6

Which type of triangle has three equal sides?

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Right-angled triangle

Answer

Scalene triangle

Question 7

What is the measure of each angle in an equilateral triangle?

Accepted Answer

60 degrees

Answer

90 degrees

Answer

120 degrees

Answer

45 degrees

Question 8

In a right-angled triangle, the hypotenuse measures 13 cm, and one of the other sides measures 5 cm. Calculate the length of the third side.

Accepted Answer

12 cm

Answer

15 cm

Answer

8 cm

Answer

10 cm

Question 9

In a triangle, the combined length of any two sides is always greater than the length of the third side. This statement is known as the:

Accepted Answer

Triangle Inequality Theorem

Answer

Angle Sum Property

Answer

Pythagoras' Theorem

Answer

Exterior Angle Property

Question 10

An equilateral triangle has three sides and three angles of equal measure. What is the measure of each angle in an equilateral triangle?

Accepted Answer

60°

Answer

45°

Answer

90°

Answer

30°

Question 11

The area of a triangle can be calculated using the formula:

Accepted Answer

1/2 * base * height

Answer

2 * base * height

Answer

1/4 * base * height

Answer

base * height

Question 12

In a triangle, the angle facing the longest side is the:

Accepted Answer

Largest angle

Answer

Right angle

Answer

Smallest angle

Answer

Obtuse angle

Question 13

Which theorem is used to establish a relationship between the lengths of the sides in a right-angled triangle?

Accepted Answer

Pythagoras' Theorem

Answer

Tangent Rule

Answer

Sine Rule

Answer

Cosine Rule

Question 14

Which of the following is NOT a property of triangles?

Accepted Answer

The sum of the exterior angles is 90 degrees

Answer

The sum of the angles in a triangle is 180 degrees

Answer

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side

Answer

The exterior angle of a triangle is equal to the sum of the opposite interior angles

Question 15

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

Accepted Answer

Pythagoras' theorem

Answer

Angle sum property

Answer

Triangle inequality theorem

Answer

Exterior angle property

Question 16

What is the area of a triangle with a base of 8 cm and a height of 6 cm?

Accepted Answer

24 square cm

Answer

48 square cm

Answer

36 square cm

Answer

12 square cm

Question 17

What is the name of the longest side of a right triangle?

Accepted Answer

Hypotenuse

Answer

Altitude

Answer

Leg

Answer

Median

Question 18

Which of the following statements about similar triangles is correct?

Accepted Answer

They have the same shape but not necessarily the same size

Answer

They have the same perimeter and the same area

Answer

They have the same size but not necessarily the same shape

Question 19

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

Accepted Answer

Angle Sum Property

Answer

Pythagoras' Theorem

Answer

Exterior Angle Property

Answer

Triangle Congruence Theorem

Question 20

A right triangle is a triangle with one angle measuring exactly:

Accepted Answer

90 degrees

Answer

60 degrees

Answer

45 degrees

Answer

120 degrees

Question 21

Which theorem relates the square of the length of the hypotenuse of a right triangle to the squares of the lengths of the other two sides?

Accepted Answer

Pythagoras' Theorem

Answer

Sine Law

Answer

Cosine Law

Answer

Triangle Inequality Theorem

Question 22

Which type of triangle has all three sides congruent?

Accepted Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Answer

Right triangle

Question 23

What is the measure of each interior angle in an equilateral triangle?

Accepted Answer

60 degrees

Answer

45 degrees

Answer

30 degrees

Answer

90 degrees

Question 24

Which of the following is NOT a method for proving triangles congruent?

Accepted Answer

Side-Side-Side (SSS) Similarity

Answer

Angle-Angle-Side (AAS) Congruence

Answer

Side-Angle-Side (SAS) Congruence

Answer

Angle-Side-Angle (ASA) Congruence

Question 25

Which of the following statements about the triangle inequality theorem is True?

Accepted Answer

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

Answer

The sum of the lengths of any two sides of a triangle is equal to the length of the third side.

Answer

The sum of the lengths of any two sides of a triangle is less than the length of the third side.

Question 26

Which of the following statements about the Pythagorean theorem is True?

Accepted Answer

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.

Answer

In a right triangle, the square of the length of the hypotenuse is equal to the difference of the squares of the lengths of the other two sides.

Question 27

Which of the following describes an equilateral triangle?

Accepted Answer

A triangle in which all three sides are of equal length.

Answer

A triangle in which only two sides are of equal length.

Answer

A triangle in which no sides are of equal length.

Question 28

Which of the following describes an isosceles triangle?

Accepted Answer

A triangle in which two sides are of equal length but the third side is different.

Answer

A triangle in which no sides are of equal length.

Answer

A triangle in which one side is much longer than the other two sides.

Answer

A triangle in which all three sides are of equal length.

Question 29

Which of the following describes a scalene triangle?

Accepted Answer

A triangle in which all three sides are of different lengths.

Answer

A triangle in which only one side is of different length.

Answer

A triangle in which two sides are of equal length and the third side is different.

Answer

A triangle in which all three sides are of equal length.

Question 30

Which of the following describes a right triangle?

Accepted Answer

A triangle in which one of the interior angles is 90 degrees.

Answer

A triangle in which all of the interior angles are less than 90 degrees.

Answer

A triangle in which all of the interior angles are equal to 90 degrees.

Answer

A triangle in which two of the interior angles are greater than 90 degrees.

Question 31

In a right triangle, the hypotenuse is:

Accepted Answer

The longest side

Answer

Perpendicular to one of the other sides

Answer

The shortest side

Answer

Equal to one of the other sides

Question 32

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

Accepted Answer

180°

Answer

90°

Answer

270°

Answer

360°

Question 33

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

Accepted Answer

Pythagoras' theorem

Answer

Similarity theorem

Answer

Triangle inequality theorem

Answer

Exterior angle property

Question 34

What is the exterior angle of a triangle formed by extending one of its sides?

Accepted Answer

The angle formed by one side of a triangle and the extension of the adjacent side

Answer

The angle formed by two opposite sides of a triangle

Answer

The angle formed by two adjacent sides of a triangle

Question 35

Which criterion for congruence of triangles states that if the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent?

Accepted Answer

SSS (side-side-side)

Answer

ASA (angle-side-angle)

Answer

AA (angle-angle)

Answer

SAS (side-angle-side)

Question 36

What is a similar triangle?

Accepted Answer

Two triangles that have the same shape but not necessarily the same size

Answer

Two triangles that have the same area but not necessarily the same shape or size

Answer

Two triangles that have the same size but not necessarily the same shape

Question 37

Which theorem states that if two triangles are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding sides?

Accepted Answer

Similarity theorem

Answer

Triangle inequality theorem

Answer

Exterior angle property

Answer

Pythagoras' theorem

Question 38

What is the area of a triangle with a base of 5 cm and a height of 3 cm?

Accepted Answer

7.5 cm²

Answer

10 cm²

Answer

20 cm²

Answer

15 cm²

Question 39

Which type of triangle has all three sides of equal length?

Accepted Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right-angled triangle

Answer

Isosceles triangle

Question 40

Which type of triangle has two sides of equal length?

Accepted Answer

Isosceles triangle

Answer

Right-angled triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Question 41

Which type of triangle has one right angle?

Accepted Answer

Right-angled triangle

Answer

Isosceles triangle

Answer

Equilateral triangle

Question 42

Which of the following statements about the exterior angle of a triangle is incorrect?

Accepted Answer

It is always less than the sum of the two remote interior angles.

Answer

It is formed by extending one side of the triangle.

Answer

It is equal to the sum of the two non-adjacent interior angles.

Question 43

A triangle with sides of lengths 5 cm, 7 cm, and 12 cm is what type of triangle?

Accepted Answer

Not possible

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Question 44

What is the name of the theorem that 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

Pythagoras' theorem

Answer

Angle sum property

Answer

Triangle inequality theorem

Answer

Euclid's theorem

Question 45

A ladder 10 meters long leans against a wall. The foot of the ladder is 6 meters away from the wall. What is the height of the wall where the ladder touches it?

Accepted Answer

8 meters

Answer

6 meters

Answer

10 meters

Question 46

A triangle with three equal sides is called:

Accepted Answer

Equilateral triangle

Answer

Right-angled triangle

Answer

Isosceles triangle

Answer

Scalene triangle