Master Triangle Geometry: Conquer Triangles with Confidence

Question 1

In a triangle, two angles measure 60° and 40°. What is the measure of the third angle?

Accepted Answer

80°

Answer

60°

Answer

100°

Question 2

Which property is NOT a characteristic of similar triangles?

Accepted Answer

Equal perimeters

Answer

Equal corresponding angles

Answer

Proportional corresponding sides

Answer

Proportional areas

Question 3

Calculate the perimeter of a triangle with sides measuring 5 cm, 7 cm, and 9 cm.

Accepted Answer

28 cm

Answer

12 cm

Answer

21 cm

Answer

33 cm

Question 4

Which property does not apply to all similar triangles?

Accepted Answer

Corresponding medians are proportional

Answer

Corresponding angles are congruent

Answer

Corresponding sides are proportional

Answer

Corresponding heights are proportional

Question 5

In a right triangle, which side is located opposite the right angle?

Accepted Answer

Opposite side

Answer

Hypotenuse

Answer

Adjacent side

Answer

Median

Question 6

State 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 + b^2 = c

Question 7

Which of the following is not an application of similar triangles?

Accepted Answer

Measuring angles

Answer

Measuring heights

Answer

Drawing scale models

Answer

Solving measurement problems

Question 8

Which of the following is **not** a method for classifying triangles based on their sides?

Accepted Answer

Obtuse

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 9

Which of the following is the correct form of the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

a² + b² - c² = 0

Question 10

Given a triangle with a perimeter of 15 cm, and two sides measuring 5 cm and 7 cm, what is the length of the third side?

Accepted Answer

10 cm

Answer

3 cm

Answer

5 cm

Answer

7 cm

Question 11

Which of the following is the definition of the altitude of a triangle?

Accepted Answer

A line segment from a vertex to the opposite side that is perpendicular to it

Answer

A side of the triangle that is perpendicular to the base

Answer

The longest side of the triangle

Answer

The shortest side of the triangle

Question 12

Which criterion is NOT used to classify triangles based solely on their sides?

Accepted Answer

Sum of angles is equal to 180°

Answer

All sides equal

Answer

Two sides equal

Answer

No sides equal

Question 13

A triangle with angles measuring 45°, 45°, and 90° is classified as a:

Accepted Answer

Right triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Answer

Equilateral triangle

Question 14

What is the correct formula to calculate the perimeter of a triangle with sides of length a, b, and c?

Accepted Answer

a + b + c

Answer

2(a + b + c)

Answer

a * b * c

Answer

The perimeter cannot be determined without knowing the angle measures.

Question 15

In a right triangle, the side opposite the right angle is known as the:

Accepted Answer

Leg

Answer

Hypotenuse

Answer

Base

Answer

Altitude

Question 16

Which theorem describes the relationship between the lengths of the sides in a right triangle, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides?

Accepted Answer

Pythagorean Theorem

Answer

Triangle Angle Sum Theorem

Answer

Triangle Similarity Theorem

Answer

Triangle Area Formula

Question 17

Which characteristic uniquely describes equilateral triangles?

Accepted Answer

Congruent sides

Answer

Congruent angles

Answer

Equal perimeter and area

Answer

Right angles

Question 18

Which criterion is essential for proving triangles similar?

Accepted Answer

Proportional side lengths

Answer

Equal side lengths

Answer

Equal angle measures

Answer

Equal area

Question 19

Determine the area of a triangle with a base of 8 cm and a height of 4 cm.

Accepted Answer

16 cm^2

Answer

12 cm^2

Answer

32 cm^2

Answer

64 cm^2

Question 20

Which inequality accurately describes the relationship between triangle side lengths a, b, and c?

Accepted Answer

a + b > c

Answer

a + b = c

Answer

a - b > c

Answer

a - b < c

Question 21

Identify the triangle that must possess a right angle.

Accepted Answer

Triangle with angles 45°, 45°, and 90°

Answer

Triangle with sides 3, 4, and 6

Answer

Triangle with angles 60°, 60°, and 60°

Answer

Triangle with sides 2, 3, and 4

Question 22

Calculate the measure of an exterior angle of a triangle with interior angles measuring 50°, 60°, and 70°.

Accepted Answer

110°

Answer

50°

Answer

60°

Answer

120°

Question 23

Which property is NOT characteristic of isosceles triangles?

Accepted Answer

Equal perimeter

Answer

Two equal sides

Answer

Two equal angles

Answer

Equal base angles

Question 24

Which set of criteria can be used to prove triangles congruent?

Accepted Answer

SSS, SAS, and ASA

Answer

SSS only

Answer

SAS and ASA only

Answer

SSS and ASA only

Question 25

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

Accepted Answer

The angle opposite the side of length 12

Answer

The angle opposite the side of length 5

Answer

The angle opposite the side of length 13

Answer

The angle that is adjacent to both the sides of length 5 and 13

Question 26

A triangle with two equal sides is classified as:

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Right

Question 27

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the:

Accepted Answer

Legs

Answer

Angles

Answer

Sides

Answer

Medians

Question 28

A triangle with equal side lengths and equal angles is known as a:

Accepted Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Answer

Obtuse

Question 29

For any triangle, the sum of its interior angles is always:

Accepted Answer

180°

Answer

90°

Answer

270°

Answer

360°

Question 30

A triangle with two right angles is called a:

Accepted Answer

Right

Answer

Obtuse

Answer

Acute

Answer

Equilateral

Question 31

Which of the following cannot be used to prove that two triangles are congruent?

Accepted Answer

Area of Similar Triangles

Answer

Side-Side-Side (SSS)

Answer

Angle-Side-Angle (ASA)

Answer

Angle-Angle-Side (AAS)

Question 32

Which theorem can be used to prove the congruence of triangles?

Accepted Answer

Angle-Angle-Side Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Sine Rule

Question 33

What is the main purpose of the Pythagorean Theorem?

Accepted Answer

To find the length of the hypotenuse of a right triangle

Answer

To find the area of a triangle

Answer

To find the perimeter of a triangle

Answer

To find the volume of a cone

Question 34

Which of these is **NOT** a property of similar triangles?

Accepted Answer

Equal perimeters

Answer

Equal angles

Answer

Proportional sides

Answer

Equal areas

Question 35

Which of the following is NOT a criterion for classifying triangles based on their sides?

Accepted Answer

All angles are equal

Answer

All three sides are equal

Answer

Two sides are equal

Answer

No sides are equal

Question 36

A triangle with one right angle is classified as:

Accepted Answer

Right

Answer

Acute

Answer

Obtuse

Answer

Equilateral

Question 37

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

Accepted Answer

Hypotenuse of a right triangle

Answer

Longest side of a triangle

Answer

Shortest side of a triangle

Answer

Altitude of a triangle

Question 38

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

Accepted Answer

1:√3

Answer

1:2

Answer

√3:2

Answer

2:√3

Question 39

The centroid of a triangle is the point where the:

Accepted Answer

Medians intersect

Answer

Altitudes intersect

Answer

Bisectors intersect

Answer

Perpendicular bisectors intersect

Question 40

Which of the following is the condition for two triangles to be similar?

Accepted Answer

Proportional sides

Answer

Equal sides

Answer

Equal sides and angles

Answer

Equal areas

Question 41

A triangle with two equal sides is known as a/an:

Accepted Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Right triangle

Question 42

Which trigonometric ratio represents the ratio of the opposite side to the adjacent side in a right triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 43

The hypotenuse of a right triangle is:

Accepted Answer

The longest side of the triangle

Answer

The side opposite the right angle

Answer

The side adjacent to the right angle

Answer

The shortest side of the triangle

Question 44

Which of the following is a theorem that relates the area of a triangle to the area of its inscribed circle?

Accepted Answer

Inscribed Circle Theorem

Answer

Pythagorean Theorem

Answer

Cosine Law

Answer

Sine Law

Question 45

A triangle with three equal sides is classified as:

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 46

Which formula is used to calculate the area of a triangle?

Accepted Answer

A = (1/2) * base * height

Answer

A = base * height

Answer

A = (1/3) * base * height

Answer

A = (1/4) * base * height

Question 47

Two triangles are similar if they have:

Accepted Answer

Equal ratios of corresponding side lengths

Answer

Equal side lengths

Answer

Equal angle measures

Answer

Equal areas

Question 48

In a right triangle, the Pythagorean theorem states that:

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

c^2 - a^2 = b^2

Answer

b^2 - a^2 = c^2

Question 49

Which of the following is a valid inequality for the side lengths of a triangle?

Accepted Answer

a + b > c

Answer

a - b < c

Answer

a * b = c

Answer

a / b > c

Question 50

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

Accepted Answer

1:√2

Answer

1:2

Answer

√2:1

Answer

2:1

Question 51

Which of the following is NOT a criterion for classifying triangles based solely on their sides?

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 52

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

Accepted Answer

Equilateral

Answer

Acute

Answer

Right

Answer

Obtuse

Question 53

If two triangles have corresponding angles that are congruent, but their corresponding sides are not proportional, can they be considered similar?

Accepted Answer

No

Answer

Yes

Answer

Only if they are equilateral

Answer

Only if they are isosceles

Question 54

In a right triangle, which side can be found using the Pythagorean theorem?

Accepted Answer

The hypotenuse only

Answer

Any side

Answer

The two shorter sides only

Answer

Cannot be determined

Question 55

What is the area of a triangle with a base of 5 units and a height of 4 units?

Accepted Answer

10 square units

Answer

5 square units

Answer

20 square units

Answer

40 square units

Question 56

Which of the following is the appropriate unit of measurement for the perimeter of a triangle?

Accepted Answer

Square meters

Answer

Cubic centimeters

Answer

Degrees

Answer

Radians

Question 57

In a right triangle, which side is the longest?

Accepted Answer

Hypotenuse

Answer

Base

Answer

Height

Question 58

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

Accepted Answer

Area

Answer

Side lengths

Answer

Angle measures

Answer

Perimeter

Question 59

A triangle has side lengths of 6 cm, 12 cm, and 13 cm. How would you classify this triangle based on its side lengths?

Accepted Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Answer

Right

Question 60

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

Accepted Answer

40 square centimeters

Answer

20 square centimeters

Answer

80 square centimeters

Answer

160 square centimeters

Question 61

Which of the following is not a defining property of similar triangles?

Accepted Answer

Corresponding altitudes are congruent.

Answer

Corresponding sides are proportional.

Answer

Corresponding angles are congruent.

Answer

The triangles have the same shape.

Question 62

Which theorem relates the altitudes and side lengths of a triangle?

Accepted Answer

Altitude-Side Triangle Theorem

Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Triangle Sum Theorem

Question 63

Which type of triangle has two equal sides?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right

Question 64

A triangle with congruent sides is classified as what?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right