Triangles: Interactive Learning Quizzes and Study Resources

Question 1

Which of the following is NOT a necessary condition for a set of three segments to form a triangle?

Accepted Answer

The sum of the lengths of any two segments must be equal to the length of the third segment.

Answer

The sum of the lengths of any two segments must be greater than the length of the third segment.

Answer

The difference between the lengths of any two segments must be less than the length of the third segment.

Answer

The difference between the lengths of any two segments must be greater than the length of the third segment.

Question 2

A triangle is classified as equilateral if

Accepted Answer

it has three equal sides.

Answer

it has two equal sides and one unequal side.

Answer

it has three unequal sides.

Answer

it has two unequal sides and one equal side.

Question 3

Which of the following theorems can be used to prove that two triangles are congruent?

Accepted Answer

SSS

Answer

Pythagorean Theorem

Answer

Cosine Law

Answer

Sine Law

Question 4

What does it mean for two triangles to be congruent?

Accepted Answer

They have the same shape and size.

Answer

They have the same shape but not necessarily the same size.

Answer

They are always equilateral.

Answer

They can be obtained only by flipping one triangle over.

Question 5

How are the Pythagorean Theorem and the Law of Cosines related? Give an example to show how these theorems connect.

Accepted Answer

The Pythagorean Theorem is a special case of the Law of Cosines that applies to right triangles.

Answer

The Law of Cosines is a specialized form of the Pythagorean Theorem that applies to non-right triangles.

Answer

The Pythagorean Theorem and the Law of Cosines are unrelated concepts.

Answer

The Law of Cosines can be used to find the area of a triangle, while the Pythagorean Theorem cannot.

Question 6

Which of the following is not a defining characteristic of triangles?

Accepted Answer

Exactly one right angle

Answer

Three line segments

Answer

Closed figure

Answer

Three interior angles

Question 7

A triangle with two congruent sides is classified as:

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Right

Question 8

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 9

Which theorem relates the lengths of the sides of a right triangle?

Accepted Answer

Pythagorean Theorem

Answer

Converse of Pythagoras Theorem

Answer

Isosceles Triangle Theorem

Answer

Triangle Inequality Theorem

Question 10

A triangle with one angle measuring more than 90 degrees is called a:

Accepted Answer

Obtuse triangle

Answer

Acute triangle

Answer

Right triangle

Answer

Equilateral triangle

Question 11

Which of the following describes a median of a triangle?

Accepted Answer

It divides a side into two congruent segments

Answer

It bisects an angle

Answer

It is perpendicular to a side

Answer

It is always shorter than any other line segment in the triangle

Question 12

What is the name of the point where the altitudes of a triangle intersect?

Accepted Answer

Orthocenter

Answer

Centroid

Answer

Incenter

Answer

Circumcenter

Question 13

Find the perimeter of a triangle with sides measuring 3 cm, 5 cm, and 7 cm.

Accepted Answer

20 cm

Answer

10 cm

Answer

15 cm

Answer

25 cm

Question 14

Which statement best defines a right triangle?

Accepted Answer

One angle measures 90 degrees.

Answer

All angles are acute.

Answer

Has equal side lengths.

Answer

Has a perimeter of 180 units.

Question 15

Which formula represents the area of a triangle?

Accepted Answer

A = (1/2) * base * height

Answer

A = base * height

Answer

A = (1/4) * base * height

Answer

A = (2/3) * base * height

Question 16

Which theorem relates the side lengths of a right triangle?

Accepted Answer

Pythagorean Theorem

Answer

Law of Sines

Answer

Law of Cosines

Answer

Triangle Inequality Theorem

Question 17

Classify the triangle with angles of 30 degrees, 60 degrees, and 90 degrees.

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 18

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

Accepted Answer

180 degrees

Answer

150 degrees

Answer

270 degrees

Answer

360 degrees

Question 19

Which triangle type exhibits a 90-degree angle?

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 20

Which formula relates the side lengths of a right triangle?

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 21

Identify the triangle type characterized by three congruent sides.

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 22

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

Accepted Answer

40 cm^2

Answer

20 cm^2

Answer

80 cm^2

Answer

160 cm^2

Question 23

Which type of triangle has all three sides of equal length?

Accepted Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Answer

Right

Question 24

Which theorem states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side?

Accepted Answer

Pythagorean Theorem

Answer

Triangle Inequality Theorem

Answer

Median Theorem

Answer

Angle Bisector Theorem

Question 25

What is the name of the theorem that states that a line segment drawn from a vertex of a triangle to the midpoint of the opposite side divides the triangle into two triangles of equal area?

Accepted Answer

Median Theorem

Answer

Angle Bisector Theorem

Answer

Altitude Theorem

Answer

Triangle Sum Theorem

Question 26

Which type of triangle has one right angle, one acute angle, and one obtuse angle?

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Question 27

Which of the following is not a property of triangles?

Accepted Answer

The Pythagorean theorem can be used to find the length of the longest side.

Answer

The sum of the interior angles is equal to 180 degrees.

Answer

The sum of the exterior angles is equal to 360 degrees.

Answer

The area of a triangle is equal to half the product of its base and height.

Question 28

What is the name of a triangle with all three sides of equal length?

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Right triangle

Question 29

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

Accepted Answer

Base × Height / 2

Answer

Base + Height / 2

Answer

Base - Height / 2

Answer

Height × Base / 2

Question 30

According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to:

Accepted Answer

The sum of the two remote interior angles

Answer

The difference of the two remote interior angles

Answer

Half of the sum of the two remote interior angles

Answer

Supplementary to the smallest remote interior angle

Question 31

Which inequality represents the Triangle Inequality Theorem?

Accepted Answer

a + b > c

Answer

a - b > c

Answer

a + b < c

Answer

a - b < c

Question 32

What is the key difference between an equilateral triangle and an isosceles triangle?

Accepted Answer

Equilateral triangles have all sides congruent, while isosceles triangles have only two sides congruent.

Answer

Equilateral triangles have all angles congruent, while isosceles triangles have only two angles congruent.

Answer

Equilateral triangles are always right triangles, while isosceles triangles are not always right triangles.

Answer

There is no difference between equilateral and isosceles triangles.

Question 33

Which of the following is NOT a property of triangles?

Accepted Answer

Four equal sides

Answer

Three sides

Answer

Three angles

Answer

Closed figure

Question 34

Classify a triangle with sides measuring 5 cm, 5 cm, and 6 cm

Accepted Answer

Isosceles triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Right triangle

Question 35

Which is the Pythagorean theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

c^2 - a^2 = b^2

Answer

a^2 - b^2 = c^2

Question 36

Classify a triangle with angles measuring 45 degrees, 45 degrees, and 90 degrees.

Accepted Answer

Right isosceles triangle

Answer

Acute triangle

Answer

Scalene triangle

Answer

Equilateral triangle

Question 37

Find the sum of the interior angles of a triangle.

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 38

Which characteristic does NOT apply to any triangle?

Accepted Answer

All angles add up to 360 degrees

Answer

All angles add up to 180 degrees

Answer

Sum of any two sides exceeds the third side

Answer

Has three sides and three angles

Question 39

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

Accepted Answer

Equilateral triangle

Answer

Right triangle

Answer

Scalene triangle

Answer

Isosceles triangle

Question 40

A triangle with one 90-degree angle is called a(n):

Accepted Answer

Right triangle

Answer

Equilateral triangle

Answer

Acute triangle

Answer

Obtuse triangle

Question 41

If two angles in a triangle measure 50 degrees and 70 degrees, what is the measure of the third angle?

Accepted Answer

60 degrees

Answer

90 degrees

Answer

120 degrees

Question 42

In triangle ABC, if AB = AC, triangle ABC is classified as:

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 43

Which of the following angle sets CANNOT form a triangle?

Accepted Answer

30 degrees, 60 degrees, 100 degrees

Answer

45 degrees, 45 degrees, 90 degrees

Answer

60 degrees, 60 degrees, 60 degrees

Answer

70 degrees, 80 degrees, 30 degrees

Question 44

The side opposite the right angle in a right triangle is called the:

Accepted Answer

Hypotenuse

Answer

Perpendicular

Answer

Altitude

Answer

Base

Question 45

If a triangle has two angles each measuring 40 degrees, what type of triangle is it?

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 46

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

Accepted Answer

180 degrees

Answer

270 degrees

Answer

360 degrees

Answer

90 degrees

Question 47

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

Accepted Answer

Acute triangle

Answer

Right triangle

Answer

Obtuse triangle

Answer

Scalene triangle

Question 48

Which statement is NOT always true about triangles?

Accepted Answer

All sides are equal in length.

Answer

A triangle always has three sides.

Answer

The sum of the interior angles always equals 180 degrees.

Answer

A triangle can have one right angle.

Question 49

A triangle has sides measuring 5 cm, 5 cm, and 7 cm. What type of triangle is it?

Accepted Answer

Isosceles triangle

Answer

Right triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Question 50

Which type of triangle is defined as having two sides of equal length?

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 51

In a triangle, one interior angle measures 70 degrees. What is the measure of the exterior angle adjacent to this angle?

Accepted Answer

110 degrees

Answer

20 degrees

Answer

70 degrees

Answer

180 degrees

Question 52

Which equation represents the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² + a² = b²

Answer

c² - b² = a²

Question 53

What is the area of a triangle with a base of 10 cm and a height of 8 cm?

Accepted Answer

40 cm²

Answer

20 cm²

Answer

80 cm²

Answer

16 cm²

Question 54

What defines a right triangle?

Accepted Answer

It has one angle that measures 90 degrees.

Answer

It has no sides of equal length.

Answer

It has two sides of equal length.

Answer

All its sides are equal in length.

Question 55

A triangle has sides measuring 6 cm, 8 cm, and 10 cm. What is its perimeter?

Accepted Answer

24 cm

Answer

14 cm

Answer

18 cm

Answer

30 cm

Question 56

Which abbreviation represents a theorem used to prove triangle similarity?

Accepted Answer

SSS

Answer

SAS

Answer

SSA

Answer

ASA

Question 57

If two triangles have congruent corresponding angles, what can you conclude about the triangles?

Accepted Answer

They are similar.

Answer

They are equilateral.

Answer

They are isometric.

Answer

They are congruent.