Triangles: Master the Basics of Geometry

Question 1

Which theorem is used to find the length of the side opposite the right angle in a right triangle?

Accepted Answer

Pythagorean Theorem

Answer

Law of Sines

Answer

Law of Cosines

Answer

Triangle Inequality Theorem

Question 2

In a triangle, the side opposite the largest angle is the:

Accepted Answer

Longest side

Answer

Shortest side

Answer

Equal to the other sides

Answer

Perpendicular to the other sides

Question 3

When comparing two similar triangles, how are their perimeters related?

Accepted Answer

Proportional to the ratio of corresponding sides

Answer

Equal

Answer

Inversely proportional to the ratio of corresponding angles

Question 4

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

Accepted Answer

Opposite

Answer

Hypotenuse

Answer

Leg

Answer

Adjacent

Question 5

The Pythagorean Theorem is used to find the length of which side of a right triangle?

Accepted Answer

Hypotenuse

Answer

Leg

Answer

Opposite

Answer

Adjacent

Question 6

Which of the following angle measures will result in an obtuse triangle?

Accepted Answer

120°, 30°, 30°

Answer

30°, 60°, 90°

Answer

45°, 45°, 90°

Answer

60°, 60°, 60°

Question 7

Using sine, which trigonometric ratio can be used to find the length of the opposite side in a right triangle?

Accepted Answer

sin θ = opposite/hypotenuse

Answer

cos θ = adjacent/hypotenuse

Answer

tan θ = opposite/adjacent

Answer

cot θ = adjacent/opposite

Question 8

Which of the following is NOT a way to classify triangles based on their angles?

Accepted Answer

Scalene

Answer

Acute

Answer

Obtuse

Answer

Right

Question 9

A triangle with side lengths of 5 cm, 12 cm, and 13 cm is classified as a:

Accepted Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Answer

Right

Question 10

In a 30-60-90 triangle, the ratio of the shortest side to the longest side is:

Accepted Answer

1:√3

Answer

1:2

Answer

√3:1

Answer

2:1

Question 11

Which of the following is NOT a valid congruence theorem for triangles?

Accepted Answer

Angle-Angle (AA)

Answer

Side-Angle-Side (SAS)

Answer

Side-Side-Side (SSS)

Answer

Angle-Side-Angle (ASA)

Question 12

Calculate the area of a triangle with a base of 10 units and a height of 8 units.

Accepted Answer

40 square units

Answer

20 square units

Answer

80 square units

Answer

160 square units

Question 13

In a right triangle, what is the term for the side opposite the right angle?

Accepted Answer

Leg

Answer

Base

Answer

Hypotenuse

Answer

Adjacent side

Question 14

Which technique is NOT used for solving triangles?

Accepted Answer

Law of Gravity

Answer

Law of Sines

Answer

Law of Cosines

Answer

Pythagorean Theorem

Question 15

A triangle with angles measuring 40°, 50°, and 90° can be classified as a:

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Question 16

In a 30-60-90 right triangle, what is the ratio of the length of the hypotenuse (c) to the length of the shorter leg (a)?

Accepted Answer

1:√2:2

Answer

√2:1:2

Answer

2:1:√2

Answer

1:2:√2

Question 17

Which property is shared by similar triangles?

Accepted Answer

Both statements (a) and (b) are true.

Answer

Corresponding sides are proportional.

Answer

Corresponding angles are congruent.

Answer

Neither statement (a) nor (b) is true.

Question 18

Calculate the measure of an exterior angle of a regular pentagon.

Accepted Answer

72 degrees

Answer

36 degrees

Answer

54 degrees

Answer

90 degrees

Question 19

Which formula represents 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 20

Which type of triangle has two congruent sides and one non-congruent side?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right

Question 21

Find the length of the side opposite the 30-degree angle in a right triangle with a hypotenuse of 10 cm.

Accepted Answer

5√3 cm

Answer

5 cm

Answer

10 cm

Answer

10√3 cm

Question 22

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

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 23

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 24

Which theorem can be used to determine if a triangle is a right triangle?

Accepted Answer

Pythagorean theorem

Answer

Sine theorem

Answer

Cosine theorem

Answer

Triangle inequality theorem

Question 25

The formula for calculating the area of a triangle is:

Accepted Answer

A = 1/2 * base * height

Answer

A = pi * radius^2

Answer

A = length * width

Answer

A = l * w * h

Question 26

A triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees is called a(n):

Accepted Answer

30-60-90 triangle

Answer

45-45-90 triangle

Answer

Equilateral triangle

Answer

Right triangle

Question 27

A triangle with all three sides of equal length is known as a(n):

Accepted Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Answer

Right triangle

Question 28

The exterior angle of a triangle is always:

Accepted Answer

Greater than the sum of the opposite interior angles

Answer

Less than the sum of the opposite interior angles

Answer

Equal to the sum of the opposite interior angles

Answer

Cannot be determined

Question 29

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

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Equilateral triangle

Question 30

Given that two sides of a triangle measure 5 cm and 7 cm, what is the minimum possible length of the third side?

Accepted Answer

4 cm

Answer

2 cm

Answer

6 cm

Answer

8 cm

Question 31

The area of a triangle with a base of 10 cm and a height of 8 cm is:

Accepted Answer

40 cm²

Answer

20 cm²

Answer

60 cm²

Answer

80 cm²

Question 32

Which equation represents the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

b² - c² = a²

Question 33

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 34

What formula calculates the area of a triangle with base 'b' and height 'h'?

Accepted Answer

(bh)/2

Answer

bh

Answer

2bh

Answer

(bh)/4

Question 35

The Pythagorean theorem establishes a relationship between the side lengths of a right triangle. Which formula represents this relationship?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

a² + c² = b²

Answer

a² - c² = b²

Question 36

In a 30-60-90 triangle, what is the measure of the smallest angle?

Accepted Answer

30 degrees

Answer

45 degrees

Answer

60 degrees

Answer

90 degrees

Question 37

In a triangle, the incenter is defined as:

Accepted Answer

The point where the angle bisectors intersect

Answer

The point where the medians intersect

Answer

The point where the perpendicular bisectors intersect

Answer

The point where the altitudes intersect

Question 38

A triangle has two angles that measure 45 degrees each. Which type of triangle is it?

Accepted Answer

Isosceles right triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Obtuse triangle

Question 39

In triangle ABC, angle A measures 30 degrees and angle B measures 60 degrees. What is the measure of angle C?

Accepted Answer

90 degrees

Answer

60 degrees

Answer

120 degrees

Answer

30 degrees

Question 40

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

Accepted Answer

24 square cm

Answer

14 square cm

Answer

48 square cm

Answer

30 square cm

Question 41

A triangle has side lengths of 5 cm, 12 cm, and 13 cm. Is this a right triangle?

Accepted Answer

Yes

Answer

Sometimes

Answer

No

Answer

Cannot be determined

Question 42

What is a defining characteristic of an equilateral triangle?

Accepted Answer

All sides are equal in length.

Answer

All angles are acute.

Answer

It has one right angle.

Answer

Opposite sides are parallel.

Question 43

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

Accepted Answer

Isosceles triangle

Answer

Right triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Question 44

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of which sides?

Accepted Answer

The other two sides

Answer

The opposite sides

Answer

The adjacent sides

Answer

The equal sides

Question 45

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

Accepted Answer

60 degrees

Answer

45 degrees

Answer

120 degrees

Answer

90 degrees

Question 46

A triangle with all three sides equal is also considered a:

Accepted Answer

Regular polygon

Answer

Trapezoid

Answer

Quadrilateral

Answer

Parallelogram

Question 47

If a triangle has an area of 24 square units and a base of 8 units, what is its height?

Accepted Answer

6 units

Answer

8 units

Answer

4 units

Answer

12 units

Question 48

What is the name of a special right triangle with angles measuring 30, 60, and 90 degrees?

Accepted Answer

30-60-90 triangle

Answer

45-45-90 triangle

Answer

60-60-60 triangle

Answer

Isosceles right triangle

Question 49

In a scalene triangle, the longest side is always opposite which angle?

Accepted Answer

The largest angle

Answer

The midpoint of the opposite side

Answer

The shortest angle

Question 50

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

Accepted Answer

All sides are equal

Answer

One angle is 90 degrees

Answer

The Pythagorean theorem applies

Question 51

Which type of triangle has three sides of equal length?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 52

In a triangle, which equation represents the Angle Sum Property?

Accepted Answer

Angles A + Angles B + Angles C = 180 degrees

Answer

Angles A * Angles B * Angles C = 180 degrees

Answer

Angles A / Angles B / Angles C = 180 degrees

Answer

Angles A - Angles B - Angles C = 180 degrees

Question 53

Which of the following is the Pythagorean theorem?

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 any triangle, the square of the sum of the lengths of two sides is equal to the square of the length of the third side.

Question 54

In a triangle with sides of length 5, 12, and 13, which side is the longest?

Accepted Answer

13

Answer

12

Answer

All sides are equal

Answer

5

Question 55

Which of the following formulas represents the area of a triangle with base b and height h?

Accepted Answer

1/2 * b * h

Answer

b - h

Answer

b + h

Answer

b * h

Question 56

Which formula represents the perimeter of a triangle with sides of length a, b, and c?

Accepted Answer

a + b + c

Answer

a - b - c

Answer

a / b / c

Answer

a * b * c

Question 57

Which of the following is a property of similar triangles?

Accepted Answer

Corresponding angles are congruent and corresponding sides are in proportion.

Answer

All angles are equal.

Answer

All sides are equal.