Master Triangle Geometry: Conquer Triangles with Confidence

Question 1

A triangle has sides measuring 5 cm, 12 cm, and 13 cm. What type of triangle is it?

Accepted Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Question 2

The Pythagorean Theorem states a relationship between the sides of a right triangle. Which equation represents this theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

a + b = c

Answer

a^2 - b^2 = c^2

Answer

a x b = c

Question 3

Which of these is NOT a way to prove that two triangles are congruent?

Accepted Answer

Angle-Side-Side (ASS)

Answer

Hypotenuse-Leg (HL)

Answer

Angle-Angle-Side (AAS)

Answer

Side-Side-Side (SSS)

Question 4

A triangle has a base of 10 cm and a height of 8 cm. What is its area?

Accepted Answer

40 square cm

Answer

80 square cm

Answer

60 square cm

Answer

20 square cm

Question 5

What is a triangle called if all three sides have the same length?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Right

Answer

Scalene

Question 6

In a right triangle, the Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of what?

Accepted Answer

Legs

Answer

Areas

Answer

Angles

Answer

Sides

Question 7

Which of these is NOT a valid classification of triangles based on their angles?

Accepted Answer

Right-Angled Obtuse Triangle

Answer

Obtuse Triangle

Answer

Acute Triangle

Answer

Right-Angled Triangle

Question 8

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

Accepted Answer

Equilateral Triangle

Answer

Scalene Triangle

Answer

Isosceles Triangle

Question 9

The sum of the interior angles of any triangle is always:

Accepted Answer

180°

Answer

360°

Answer

270°

Answer

90°

Question 10

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

Accepted Answer

Isosceles Triangle

Answer

Scalene Triangle

Answer

Right-Angled Triangle

Answer

Equilateral Triangle

Question 11

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

Accepted Answer

Hypotenuse

Answer

Base

Answer

Perpendicular

Answer

Altitude

Question 12

Which of the following is the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a + b² = c

Answer

a² - b² = c²

Answer

a + b = c

Question 13

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

Accepted Answer

All sides are equal.

Answer

No angles are equal.

Answer

All angles are different.

Answer

No sides are equal.

Question 14

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

It varies depending on the triangle type.

Answer

360 degrees

Question 15

A triangle with one angle measuring 90 degrees is called a...

Accepted Answer

Right triangle

Answer

Obtuse triangle

Answer

Equilateral triangle

Answer

Acute triangle

Question 16

In a triangle, the longest side is always opposite the...

Accepted Answer

Largest angle

Answer

Right angle

Answer

Smallest angle

Answer

It depends on the triangle type.

Question 17

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to...

Accepted Answer

The sum of the squares of the other two sides

Answer

The difference of the squares of the other two sides

Answer

The square root of the sum of the squares of the other two sides

Answer

The product of the squares of the other two sides

Question 18

A ladder 10 meters long leans against a wall. The base of the ladder is 6 meters away from the wall. What is the height the ladder reaches on the wall?

Accepted Answer

8 meters

Answer

10 meters

Answer

6 meters

Answer

16 meters

Question 19

Two triangles are said to be similar if...

Accepted Answer

Their corresponding angles are equal, and their corresponding sides are proportional

Answer

They have the same size

Answer

They have the same shape

Question 20

Which of the following is NOT a valid classification of triangles based on their angles?

Accepted Answer

Right-Obtuse Triangle

Answer

Acute Triangle

Answer

Obtuse Triangle

Answer

Right Triangle

Question 21

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

Accepted Answer

Equilateral Triangle

Answer

Right Triangle

Answer

Scalene Triangle

Answer

Isosceles Triangle

Question 22

The sum of the interior angles of any triangle is always:

Accepted Answer

180 degrees

Answer

360 degrees

Answer

90 degrees

Answer

It varies depending on the triangle

Question 23

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

Accepted Answer

Hypotenuse

Answer

Base

Answer

Altitude

Answer

Perpendicular

Question 24

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

Accepted Answer

Isosceles Triangle

Answer

Right Triangle

Answer

Scalene Triangle

Answer

Equilateral Triangle

Question 25

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to:

Accepted Answer

The sum of the squares of the other two sides

Answer

The square root of the sum of the squares of the other two sides

Answer

The product of the squares of the other two sides

Answer

The difference of the squares of the other two sides

Question 26

A triangle with one angle measuring 90 degrees is called a(n):

Accepted Answer

Right Triangle

Answer

Acute Triangle

Answer

Equilateral Triangle

Answer

Obtuse Triangle

Question 27

If a right triangle has sides of length 3 cm, 4 cm, and 5 cm, what is the length of the hypotenuse?

Accepted Answer

5 cm

Answer

4 cm

Answer

7 cm

Answer

3 cm

Question 28

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

Accepted Answer

Acute Triangle

Answer

Obtuse Triangle

Answer

Isosceles Triangle

Answer

Right Triangle

Question 29

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

Accepted Answer

180 degrees

Answer

270 degrees

Answer

90 degrees

Answer

360 degrees

Question 30

Which type of triangle has exactly one right angle?

Accepted Answer

Right triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Answer

Acute triangle

Question 31

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

Accepted Answer

1/2 * base * height

Answer

base * height

Answer

base + height

Answer

base - height

Question 32

What is the Pythagorean Theorem used for?

Accepted Answer

Finding the length of the hypotenuse in a right triangle

Answer

Classifying triangles

Answer

Finding the area of a triangle

Question 33

Which of the following triangles is similar to a triangle with sides 3, 4, and 5?

Accepted Answer

6, 8, 10

Answer

3, 5, 7

Answer

5, 7, 9

Answer

4, 5, 6

Question 34

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

Accepted Answer

Hypotenuse

Answer

Base

Answer

Leg

Answer

Height

Question 35

Which of the following is a property of an isosceles triangle?

Accepted Answer

Two equal sides

Answer

Three equal sides

Answer

Four equal sides

Question 36

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

Accepted Answer

360 degrees

Answer

180 degrees

Answer

540 degrees

Answer

270 degrees

Question 37

Which of the following is NOT a method for classifying triangles?

Accepted Answer

By perimeter

Answer

By area

Answer

By angles

Answer

By sides