Triangles: Master the Basics of Triangles in Geometry

Question 1

Which of the following is NOT a type of triangle based on side lengths?

Accepted Answer

Equiangular

Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Question 2

A triangle with two equal sides is known as a:

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right

Question 3

Which type of triangle has three acute angles?

Accepted Answer

Acute

Answer

Obtuse

Answer

Right

Answer

Equilateral

Question 4

Which trigonometric ratio is used to find the sine of an angle in a triangle?

Accepted Answer

Sin θ = Opposite / Hypotenuse

Answer

Cos θ = Adjacent / Hypotenuse

Answer

Tan θ = Opposite / Adjacent

Answer

Csc θ = Hypotenuse / Opposite

Question 5

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

Accepted Answer

Opposite

Answer

Hypotenuse

Answer

Adjacent

Answer

Base

Question 6

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

Accepted Answer

It relates the squares of the sides in a right triangle.

Answer

It applies to all triangles.

Answer

It can be used to find the area of any triangle.

Answer

It was discovered by Euclid.

Question 7

The Pythagorean theorem is used to calculate the length of the:

Accepted Answer

Hypotenuse of a right triangle

Answer

Legs of a right triangle

Answer

Area of a right triangle

Answer

Perimeter of a right triangle

Question 8

Which of the following formulas calculates the area of a triangle?

Accepted Answer

A = (1/2)bh

Answer

A = ½lw

Answer

A = πr²

Answer

A = 4πr²

Question 9

A triangle with angles measuring 30, 60, and 90 degrees is classified as a:

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Question 10

Which of the following triangles cannot be constructed with the given side lengths: 3, 4, and 7 units?

Accepted Answer

Cannot be determined

Answer

Acute triangle

Answer

Right triangle

Answer

Obtuse triangle

Question 11

Which type of triangle is NOT classified based on its sides?

Accepted Answer

Right

Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Question 12

A triangle with angles measuring 90°, 60°, and 30° is classified as what type of triangle by its angles?

Accepted Answer

Right

Answer

Acute

Answer

Equilateral

Answer

Obtuse

Question 13

Which of the following formulas calculates the area of a triangle?

Accepted Answer

A = (1/2) * base * height

Answer

A = base * height

Answer

A = π * radius²

Answer

A = side²

Question 14

Calculate the perimeter of a triangle with side lengths of 5 cm, 7 cm, and 10 cm.

Accepted Answer

22 cm

Answer

15 cm

Answer

25 cm

Answer

30 cm

Question 15

Which type of triangle has three unequal sides?

Accepted Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Right triangle

Question 16

Which theorem helps determine if a triangle is right-angled?

Accepted Answer

Pythagorean Theorem

Answer

Cosine Rule

Answer

Sine Rule

Answer

Triangle Inequality Theorem

Question 17

Which statement about triangles is NOT true?

Accepted Answer

An exterior angle of a triangle is always smaller than either of the opposite interior angles.

Answer

All triangles have three sides.

Answer

The angles inside a triangle always add up to 180 degrees.

Answer

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

Question 18

Identify the defining characteristic of a right triangle:

Accepted Answer

One right angle

Answer

Equal angles

Answer

180-degree interior angle sum

Answer

Hypotenuse squared equals the sum of the other two sides squared

Question 19

Which of the following is NOT a property of an isosceles triangle?

Accepted Answer

Equal all three sides

Answer

Two equal sides

Answer

Two congruent base angles

Answer

Equal opposite angles

Question 20

Determine 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

48 cm²

Answer

96 cm²

Question 21

Identify the triangle with two congruent sides:

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Obtuse

Question 22

Calculate the perimeter of a scalene triangle with side lengths of 4 cm, 7 cm, and 9 cm:

Accepted Answer

28 cm

Answer

12 cm

Answer

20 cm

Answer

36 cm

Question 23

Which of the following is NOT a valid triangle classification based on sides?

Accepted Answer

Pythagorean

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 24

Which of the following angles cannot exist in a triangle?

Accepted Answer

150 degrees

Answer

45 degrees

Answer

60 degrees

Answer

120 degrees

Question 25

Calculate the area of a triangle with a base of 5 cm and a height of 3 cm.

Accepted Answer

10 cm^2

Answer

8 cm^2

Answer

15 cm^2

Answer

20 cm^2

Question 26

What is the primary purpose of the Pythagorean theorem?

Accepted Answer

Determining the length of a triangle side

Answer

Finding the area of a triangle

Answer

Calculating the perimeter of a triangle

Answer

Measuring the angles in a triangle

Question 27

Which of the following inequalities represents the triangle inequality theorem?

Accepted Answer

a + b ≥ c

Answer

a + b < c

Answer

a - b > c

Answer

a - b ≤ c

Question 28

What is the total measure of the interior angles in a triangle?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 29

Which of the following triangles has the largest area?

Accepted Answer

Triangle with a base of 6 cm and a height of 4 cm

Answer

Triangle with a base of 8 cm and a height of 3 cm

Answer

Triangle with a base of 10 cm and a height of 2 cm

Answer

Triangle with a base of 12 cm and a height of 1 cm

Question 30

What are the special relationships between the sides and angles of a 45-45-90 triangle?

Accepted Answer

The legs are equal in length, and the hypotenuse is √2 times the length of a leg

Answer

The legs are twice the length of the hypotenuse

Answer

The hypotenuse is the longest side, and the angles opposite the legs are 45 degrees

Answer

The sum of the two acute angles is 90 degrees

Question 31

Which theorem is unrelated to triangles?

Accepted Answer

Binomial Theorem

Answer

Pythagorean Theorem

Answer

Sine Law

Answer

Cosine Law

Question 32

What is the sum of interior angles in any triangle?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

120 degrees

Answer

270 degrees

Question 33

What type of triangle has one right angle?

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 34

Which theorem is not applicable to triangles?

Accepted Answer

Fundamental Theorem of Calculus

Answer

Pythagorean Theorem

Answer

Angle Bisector Theorem

Answer

Law of Sines

Question 35

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

Accepted Answer

Area

Answer

Angle measure

Answer

Number of congruent sides

Answer

Side length

Question 36

A triangle with three equal sides is known as a:

Accepted Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Answer

Isosceles triangle

Question 37

Which type of triangle has one right angle?

Accepted Answer

Right triangle

Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Obtuse triangle

Question 38

Which mathematical equation represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

a - b = c

Answer

a/b = c

Question 39

The sum of the interior angles of a triangle is equal to:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

360 degrees

Answer

270 degrees

Question 40

A triangle with two congruent angles is classified as:

Accepted Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Right triangle

Question 41

The altitude of a triangle is the perpendicular distance from a vertex to which part of the triangle?

Accepted Answer

The opposite side

Answer

The hypotenuse

Answer

The adjacent side

Question 42

Which of these describes how triangles are **NOT** classified?

Accepted Answer

Acute and Obtuse

Answer

Right

Answer

Isosceles

Answer

Equilateral

Question 43

Which equation represents the Pythagorean theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

V = l * w * h

Answer

s = 1/2 * b * h

Answer

A = 1/2 * d1 * d2

Question 44

What type of triangle has two sides of equal length?

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Right

Question 45

What kind of triangle has all sides equal?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 46

What is the total measure of the interior angles of any triangle?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

360 degrees

Answer

270 degrees

Question 47

Which theorem connects the sides and angles of a right triangle?

Accepted Answer

Pythagorean theorem

Answer

Sine theorem

Answer

Tangent theorem

Answer

Cosine theorem

Question 48

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

Accepted Answer

Equiangular

Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Question 49

A triangle with two equal sides and one distinct side is classified as:

Accepted Answer

Isosceles

Answer

Right

Answer

Equilateral

Answer

Scalene

Question 50

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

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Sine Rule

Answer

Cosine Rule

Question 51

The area of a triangle with base 'b' and height 'h' is given by:

Accepted Answer

0.5 * b * h

Answer

0.25 * b * h

Answer

b * h

Answer

2 * b * h

Question 52

The perimeter of a triangle with sides 'a', 'b', and 'c' is:

Accepted Answer

a + b + c

Answer

0.5 * a * b * c

Answer

2 * a * b * c

Answer

a^2 + b^2 + c^2

Question 53

Which of the following is a special triangle with all sides equal?

Accepted Answer

Equilateral

Answer

Scalene

Answer

Right

Answer

Isosceles

Question 54

A triangle with one right angle is known as a:

Accepted Answer

Right triangle

Answer

Obtuse triangle

Answer

Equiangular triangle

Answer

Acute triangle

Question 55

The Pythagorean theorem is only applicable to:

Accepted Answer

Right triangles

Answer

Isosceles triangles

Answer

All triangles

Answer

Equilateral triangles

Question 56

Which of the following is NOT a method for solving for unknown sides or angles in a triangle?

Accepted Answer

Distance Formula

Answer

Cosine Rule

Answer

Sine Rule

Answer

Pythagorean Theorem

Question 57

The Sine Rule states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is:

Accepted Answer

Constant

Answer

Zero

Answer

Variable

Answer

Infinity