Master Triangle Geometry: Online Quizzes and Practice

Question 1

Which characteristic defines an isosceles triangle?

Accepted Answer

Two equal sides

Answer

Three equal sides

Answer

Three right angles

Answer

No equal sides

Question 2

Identify the accurate description of an equilateral triangle:

Accepted Answer

Three equal angles and sides

Answer

Three right angles and three equal sides

Answer

Three equal angles and unequal sides

Answer

Three right angles and unequal sides

Question 3

A triangle containing a 90-degree angle is called a:

Accepted Answer

Right triangle

Answer

Obtuse triangle

Answer

Acute triangle

Answer

Equilateral triangle

Question 4

Which of the following is NOT a valid criterion for categorizing triangles?

Accepted Answer

Length of diagonals

Answer

Length of sides

Answer

Measure of angles

Answer

Number of equal sides

Question 5

A triangle with two equal sides is known as a:

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right-angled triangle

Question 6

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

Accepted Answer

28 cm

Answer

10 cm

Answer

18 cm

Answer

36 cm

Question 7

Determine the type of triangle that has angles measuring 45°, 45°, and 90°.

Accepted Answer

Right-angled triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Isosceles triangle

Question 8

Which of the following side length combinations cannot form a triangle?

Accepted Answer

2 cm, 5 cm, 6 cm

Answer

3 cm, 4 cm, 5 cm

Answer

4 cm, 6 cm, 10 cm

Answer

5 cm, 7 cm, 11 cm

Question 9

Which type of triangle has two sides of equal length?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right

Question 10

If the height of a triangle is doubled while the base remains unchanged, what happens to its area?

Accepted Answer

It doubles

Answer

It triples

Answer

It remains the same

Answer

It halves

Question 11

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 12

Which method is NOT used to solve problems involving similar triangles?

Accepted Answer

Pythagorean theorem

Answer

Proportionality theorem

Answer

Law of Sines

Answer

Law of Cosines

Question 13

Which of the following is not a criterion used to classify triangles?

Accepted Answer

Area

Answer

Number of sides

Answer

Length of sides

Answer

Measure of angles

Question 14

Which formula represents the area of a triangle?

Accepted Answer

A = (1/2) * base * height

Answer

A = length * width

Answer

A = π * radius²

Answer

A = side²

Question 15

Two triangles are considered similar if they share which property?

Accepted Answer

Equal side lengths and equal angles

Answer

Equal side lengths and different angles

Answer

Different side lengths and equal angles

Answer

Different side lengths and different angles

Question 16

The Pythagorean theorem is primarily used to determine the length of which side in a right triangle?

Accepted Answer

Hypotenuse

Answer

Base

Answer

Altitude

Answer

Leg

Question 17

Which of the following is NOT a type of triangle based on its sides?

Accepted Answer

Obtuse

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 18

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

Accepted Answer

A = 1/2 * base * height

Answer

A = base * height

Answer

A = 1/2 * base + height

Answer

A = base - height

Question 19

A triangle with two congruent angles is classified as a:

Accepted Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Right triangle

Question 20

The theorem that states the sum of the interior angles of a triangle is 180 degrees is known as the:

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Distance Formula

Answer

Angle Bisector Theorem

Question 21

A triangle with no congruent sides or angles is called a:

Accepted Answer

Scalene triangle

Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Regular triangle

Question 22

Which type of triangle has all sides of equal length?

Accepted Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Answer

Right

Question 23

Which angle in a triangle is always less than 90 degrees?

Accepted Answer

Acute angle

Answer

Obtuse angle

Answer

Right angle

Answer

Straight angle

Question 24

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

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Area of Triangles Theorem

Answer

Similar Triangles Theorem

Question 25

What condition must be met for two triangles to be considered similar?

Accepted Answer

Equal angles but not necessarily equal side lengths

Answer

Equal side lengths

Answer

Equal area

Answer

Equal perimeter

Question 26

Which type of triangle has two congruent angles?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right

Question 27

In a right triangle, which term describes the side opposite the right angle?

Accepted Answer

Leg

Answer

Base

Answer

Height

Answer

Hypotenuse

Question 28

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

Accepted Answer

(1/2) * base * height

Answer

(1/2) * base + height

Answer

base * height

Answer

base / height

Question 29

Triangles that have the same shape, but not necessarily the same size, are called:

Accepted Answer

Similar triangles

Answer

Isosceles triangles

Answer

Scalene triangles

Answer

Equilateral triangles

Question 30

Which type of triangle has three congruent sides?

Accepted Answer

Equilateral triangle

Answer

Right triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Question 31

The sum of the interior angles of a triangle is:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 32

If one angle of a triangle measures 60 degrees, what is the maximum possible value of the largest angle?

Accepted Answer

120 degrees

Answer

60 degrees

Answer

90 degrees

Answer

150 degrees

Question 33

The area of a triangle is 24 square cm. If its base is 8 cm, what is its height?

Accepted Answer

4 cm

Answer

3 cm

Answer

6 cm

Answer

8 cm

Question 34

Which of the following is **not** a classification of triangles based on sides?

Accepted Answer

Obtuse

Answer

Scalene

Answer

Equilateral

Answer

Isosceles

Question 35

Triangles are similar if they have:

Accepted Answer

Corresponding angles that are congruent

Answer

Equal side lengths

Answer

The same number of sides

Answer

Congruent base angles

Question 36

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

Accepted Answer

Triangle Sum Theorem

Answer

Law of Sines

Answer

Pythagorean Theorem

Answer

Law of Cosines

Question 37

What is the formula for the area of a triangle?

Accepted Answer

Area = (1/2) * base * height

Answer

Area = (1/3) * base * height

Answer

Area = (1/4) * base * height

Answer

Area = base * height

Question 38

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

Accepted Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Answer

Isosceles triangle

Question 39

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 40

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

Accepted Answer

Right triangle

Answer

Equilateral triangle

Answer

Obtuse triangle

Answer

Acute triangle

Question 41

A triangle with sides of length 5 cm, 7 cm, and 10 cm is classified as a(n):

Accepted Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Right triangle

Answer

Isosceles triangle

Question 42

The formula for calculating the area of a triangle is:

Accepted Answer

(1/2) * base * height

Answer

base + height

Answer

(1/2) * (base + height)

Answer

base * height

Question 43

What is the perimeter of a triangle with sides measuring 4 cm, 6 cm, and 8 cm?

Accepted Answer

18 cm

Answer

12 cm

Answer

24 cm

Answer

10 cm

Question 44

Two triangles are considered similar if they have:

Accepted Answer

The same shape but different sizes

Answer

Two equal angles

Answer

The same size but different shapes

Answer

All sides equal

Question 45

In similar triangles, the ratio of their corresponding sides is:

Accepted Answer

The same

Answer

Inversely proportional

Answer

Always 1:1

Answer

Different

Question 46

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

Accepted Answer

Obtuse triangle

Answer

Right triangle

Answer

Isosceles triangle

Answer

Acute triangle

Question 47

If two triangles have two pairs of congruent angles and one pair of congruent sides, we can conclude that:

Accepted Answer

The triangles are similar

Answer

The triangles are congruent

Answer

The triangles are right triangles

Answer

There is not enough information to conclude anything