Triangle Properties: Master the Basics of Triangles

Question 1

Which of the following is NOT a characteristic of all triangles?

Accepted Answer

All triangles have the same area.

Answer

All triangles have at least two congruent angles.

Answer

All interior angles add up to 180 degrees.

Answer

All triangles have at least two congruent sides.

Question 2

What is the name of the theorem that states the sum of the interior angles of a triangle is always 180 degrees?

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Similarity Theorem

Answer

Congruence Theorem

Question 3

In a right triangle, which side is always the longest?

Accepted Answer

Hypotenuse

Answer

Opposite side

Answer

Median

Answer

Adjacent side

Question 4

What is the name of a line segment connecting two vertices of a triangle?

Accepted Answer

Side

Answer

Height

Answer

Edge

Answer

Radius

Question 5

What is the formula for calculating the area of a triangle with base 'b' and height 'h'?

Accepted Answer

0.5 * b * h

Answer

2 * b * h

Answer

0.25 * b * h

Answer

b * h

Question 6

Two triangles have the same shape but not necessarily the same size. How would you classify them?

Accepted Answer

Similar

Answer

Equivalent

Answer

Congruent

Answer

Identical

Question 7

A triangle with three unequal sides is known as:

Accepted Answer

Scalene

Answer

Equilateral

Answer

Isosceles

Question 8

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

Accepted Answer

180 degrees

Answer

360 degrees

Answer

90 degrees

Answer

270 degrees

Question 9

The Pythagorean theorem states that 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:

Accepted Answer

Legs

Answer

Altitudes

Answer

Angles

Answer

Medians

Question 10

The formula for calculating the area of a triangle is:

Accepted Answer

0.5 * base * height

Answer

2 * base * height

Answer

base * height

Answer

0.75 * base * height

Question 11

A triangle with two equal sides and one unequal side is called a:

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Question 12

Which property is not a characteristic of all triangles?

Accepted Answer

All sides are equal in length.

Answer

Opposing angles are congruent.

Answer

The sum of the exterior angles is 360 degrees.

Answer

The sum of the interior angles is 180 degrees.

Question 13

In a triangle, the side with the greatest length is opposite the:

Accepted Answer

Largest angle.

Answer

Smallest angle.

Answer

Right angle.

Question 14

Calculate the area of a triangle with a base of 8 cm and a height of 6 cm.

Accepted Answer

24 square cm.

Answer

12 square cm.

Answer

48 square cm.

Answer

36 square cm.

Question 15

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

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Right triangle

Answer

Scalene triangle

Question 16

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

Accepted Answer

180 degrees

Answer

360 degrees

Answer

It varies depending on the triangle

Answer

90 degrees

Question 17

Two triangles are congruent if they have:

Accepted Answer

All corresponding sides and angles equal

Answer

All corresponding angles equal

Answer

Two corresponding angles and one corresponding side equal

Answer

Two corresponding sides and one corresponding angle equal

Question 18

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

Accepted Answer

Isosceles

Answer

Scalene

Answer

Right

Answer

Equilateral

Question 19

The Pythagorean theorem states that in a right triangle:

Accepted Answer

The square of the hypotenuse is equal to the sum of the squares of the other two sides

Answer

The square of the hypotenuse is equal to the product of the other two sides

Answer

The sum of the squares of all three sides is equal

Question 20

Two triangles are congruent if they have:

Accepted Answer

Same shape and size

Answer

Same side lengths

Answer

Same area

Answer

Same angles

Question 21

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 hypotenuse?

Accepted Answer

Pythagorean Theorem

Answer

Converse of the Pythagorean Theorem

Answer

Angle Bisector Theorem

Answer

Triangle Inequality Theorem

Question 22

Two triangles are similar if they:

Accepted Answer

Have the same shape but not necessarily the same size

Answer

Have the same angles

Answer

Have the same side lengths

Question 23

If the area of a triangle is 24 square units and its base is 6 units, what is its height?

Accepted Answer

8 units

Answer

12 units

Answer

4 units

Answer

16 units

Question 24

Which of the following special triangles has a ratio of side lengths 3:4:5?

Accepted Answer

Pythagorean triple

Answer

Scalene triangle

Answer

Equilateral triangle

Answer

Isosceles triangle

Question 25

The measure of an exterior angle of a triangle is equal to the sum of the measures of the:

Accepted Answer

Remote interior angles

Answer

Opposite interior angles

Answer

Adjacent interior angles

Answer

Same-side interior angles

Question 26

If the midpoint of a side of a triangle divides the side into a ratio of 2:3, what is the ratio of the areas of the two triangles formed?

Accepted Answer

4:9

Answer

6:7

Answer

2:3

Answer

1:4

Question 27

Which of the following is a condition for a triangle to be isosceles?

Accepted Answer

Two sides are equal

Answer

Two angles are equal

Answer

Three angles are equal

Answer

Three sides are equal

Question 28

In a right triangle, the hypotenuse is:

Accepted Answer

The longest side

Answer

Adjacent to the right angle

Answer

The shortest side

Answer

Opposite the right angle

Question 29

In a triangle, the sum of the interior angles is always:

Accepted Answer

180 degrees

Answer

360 degrees

Answer

270 degrees

Answer

90 degrees

Question 30

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

Accepted Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Right triangle

Answer

Scalene triangle

Question 31

If two triangles have the same shape but different sizes, they are considered:

Accepted Answer

Similar

Answer

Congruent

Answer

Scalene

Answer

Isosceles

Question 32

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

Accepted Answer

Hypotenuse

Answer

Base

Answer

Altitude

Answer

Perpendicular

Question 33

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

Accepted Answer

They are similar

Answer

They are right triangles

Answer

They have the same area

Answer

They are congruent

Question 34

Two triangles are congruent if they have:

Accepted Answer

All three sides and all three angles congruent

Answer

Two angles and the included side congruent

Answer

Two sides and the included angle congruent

Answer

Two sides and a non-included angle congruent

Question 35

In a triangle ABC, if AB = AC and angle B = 60 degrees, what type of triangle is it?

Accepted Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Answer

Isosceles triangle

Question 36

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

Accepted Answer

Right triangle

Answer

Scalene triangle

Answer

Acute triangle

Answer

Obtuse triangle