Master Triangles in Geometry: Interactive Quizzes and Practice

Question 1

Which of the following is NOT a type of triangle classified by its side lengths?

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 2

What is the defining characteristic of scalene triangles?

Accepted Answer

Different side lengths

Answer

Equal side lengths

Answer

Equal angles

Answer

A 90-degree angle

Question 3

Which fundamental property applies to all triangles?

Accepted Answer

The sum of their interior angles equals 180 degrees.

Answer

Their bases are always congruent.

Answer

They can have two obtuse angles.

Answer

Their area is always larger than the area of a square with the same perimeter.

Question 4

According to the Side-Side-Side (SSS) Congruence Theorem, what condition must be met for two triangles to be considered congruent?

Accepted Answer

All three sides of each triangle are equal in length.

Answer

Two sides and one angle of each triangle are congruent.

Answer

All three angles of each triangle are congruent.

Answer

The areas of the two triangles are equal.

Question 5

Which of the following is NOT a type of triangle classified by its side lengths?

Accepted Answer

Obtuse

Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Question 6

Which of the following is not a type of triangle?

Accepted Answer

Trapezoid

Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Question 7

Which shape is not a triangle?

Accepted Answer

Quadrilateral

Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Question 8

Which figure is different from the others?

Accepted Answer

Hexagon

Answer

Equilateral triangle

Answer

Isosceles triangle

Answer

Scalene triangle

Question 9

In the realm of triangle congruence theorems, which theorem is the exception?

Accepted Answer

AA (Angle-Angle)

Answer

SSS (Side-Side-Side)

Answer

ASA (Angle-Side-Angle)

Answer

SAS (Side-Angle-Side)

Question 10

Which congruence theorems can be used to prove that two triangles are congruent?

Accepted Answer

SSS (Side-Side-Side)

Accepted Answer

SAS (Side-Angle-Side)

Accepted Answer

ASA (Angle-Side-Angle)

Answer

Hinge Theorem

Question 11

Which of the following is NOT a congruence theorem for triangles? A congruence theorem states that if certain parts of two triangles are congruent, then the triangles are congruent as a whole.

Accepted Answer

AAS (Angle-Angle-Side)

Answer

SSS (Side-Side-Side)

Answer

SAS (Side-Angle-Side)

Answer

ASA (Angle-Side-Angle)

Question 12

In a triangle, which of the following is always true about the sum of the lengths of its three sides?

Accepted Answer

It is greater than the length of any one side.

Answer

It is less than the length of any one side.

Answer

It is equal to the length of any one side.

Question 13

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

Accepted Answer

Right

Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Question 14

In triangle ABC, if AB is equal in length to BC, what property does triangle ABC have?

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Right-angled

Answer

Scalene

Question 15

Given that one side of a triangle measures 5 cm and the sum of the other two sides is 12 cm, what is the range of possible lengths for the missing side?

Accepted Answer

1 cm < x < 7 cm

Answer

x < 1 cm or x > 7 cm

Answer

0 cm < x < 12 cm

Answer

x > 12 cm

Question 16

Which type of triangle has three sides of different lengths?

Accepted Answer

Scalene Triangle

Answer

Equilateral Triangle

Answer

Isosceles Triangle

Answer

Right Triangle

Question 17

In a right triangle, the altitude drawn to the hypotenuse divides the triangle into two smaller triangles. Which of the following statements about the altitude is true?

Accepted Answer

The altitude is perpendicular to the hypotenuse.

Answer

The altitude divides the hypotenuse into two equal segments.

Answer

The altitude is the longest side of the triangle.

Answer

The altitude is parallel to the hypotenuse.

Question 18

According to the triangle inequality theorem, if the sum of the lengths of two sides of a triangle is less than the length of the third side, can the triangle exist?

Accepted Answer

No, the triangle cannot exist.

Answer

Yes, the triangle can exist.

Answer

The triangle can only exist if it is a right triangle.

Answer

The triangle can only exist if it is an isosceles triangle.

Question 19

What's the total measure of the three interior angles in any triangle?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Question 20

A farmer has 100 meters of fencing to enclose a rectangular field. What is the largest area the farmer can enclose with the fencing?

Accepted Answer

2500 square meters

Answer

1250 square meters

Answer

5000 square meters

Answer

10000 square meters

Question 21

Besides being a rectangle, a square also shares the properties of which other geometric shape?

Accepted Answer

Rhombus

Answer

Equilateral Triangle

Answer

Circle

Answer

Trapezoid

Question 22

In a non-right triangle, how can the law of sines be used to find unknown side lengths and angles?

Accepted Answer

By using the ratio of the sine of an angle to the length of its opposite side

Answer

The law of sines cannot be used in non-right triangles

Answer

By using the cosine ratio to determine unknown angles and side lengths

Question 23

Which criteria must be met for two triangles to be considered similar?

Accepted Answer

Their corresponding angles are congruent and their corresponding sides are proportional.

Answer

Their corresponding angles are congruent.

Answer

Their corresponding sides are proportional.

Answer

They have equal areas.

Question 24

Two triangles have two pairs of corresponding sides that are equal in length, but the angles between these sides are not equal. What can you logically conclude?

Accepted Answer

The triangles are similar but not congruent.

Answer

The triangles are congruent.

Question 25

If a median of a triangle is also an angle bisector, what can you conclude about the triangle?

Accepted Answer

The triangle is isosceles.

Answer

The triangle is scalene.

Answer

The given information is insufficient to determine whether the triangle is isosceles or scalene.

Question 26

In a triangle, the sum of the measures of two of its angles is equal to the measure of the third angle. Which type of triangle is this?

Accepted Answer

Right

Answer

Scalene

Answer

Isosceles

Answer

Equilateral

Question 27

A triangle with two equal sides is known as a:

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 28

Which condition must be met for a triangle to be considered a right triangle?

Accepted Answer

The square of one side equals the sum of the squares of the other two sides

Answer

The sum of two angles is 90°

Answer

The three sides are all equal in length

Answer

The triangle has two parallel sides

Question 29

Classify a triangle with sides measuring 3 cm, 4 cm, and 5 cm.

Accepted Answer

Scalene

Answer

Acute

Answer

Obtuse

Answer

Right

Question 30

Calculate the perimeter of a triangle with side lengths of 6 cm, 8 cm, and 10 cm.

Accepted Answer

32 cm

Answer

14 cm

Answer

24 cm

Answer

48 cm

Question 31

Identify the type of triangle with angles measuring 45°, 45°, and 90°.

Accepted Answer

Right

Answer

Equilateral

Answer

Isosceles

Answer

Scalene

Question 32

Calculate the height of a triangle with an area of 24 cm² and a base of 8 cm.

Accepted Answer

6 cm

Answer

3 cm

Answer

12 cm

Answer

24 cm

Question 33

Which type of triangle has two sides of equal length?

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right triangle

Question 34

Find the measure of the third angle in a triangle if two angles measure 40° and 70°.

Accepted Answer

110°

Answer

50°

Answer

70°

Answer

180°

Question 35

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

Accepted Answer

Leg

Answer

Hypotenuse

Answer

Median

Answer

Altitude

Question 36

Which side length of a right triangle can be determined using the Pythagorean theorem?

Accepted Answer

Hypotenuse

Answer

Leg

Answer

Altitude

Answer

Median

Question 37

The sum of the interior angles of a triangle equals:

Accepted Answer

180 degrees

Answer

90 degrees

Answer

120 degrees

Answer

270 degrees

Question 38

In a scalene triangle, the longest side is always opposite the:

Accepted Answer

Largest angle

Answer

Smallest angle

Answer

Right angle

Answer

Obtuse angle

Question 39

An equilateral triangle has:

Accepted Answer

Three equal angles and three equal sides

Answer

Three equal angles and two equal sides

Answer

Two equal angles and three equal sides

Answer

Two equal angles and two equal sides

Question 40

Which type of triangle is the Pythagorean theorem specifically applicable to?

Accepted Answer

Right

Answer

Acute

Answer

Obtuse

Answer

Equilateral

Question 41

Which of the following is NOT a type of angle commonly found in triangles?

Accepted Answer

Straight

Answer

Acute

Answer

Right

Answer

Obtuse

Question 42

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

Accepted Answer

180 degrees

Answer

90 degrees

Answer

120 degrees

Answer

270 degrees

Question 43

Which property is shared by all isosceles triangles?

Accepted Answer

Two equal sides

Answer

Two equal angles

Answer

Three equal angles

Answer

Three equal sides

Question 44

A triangle with one 90-degree angle is classified as a:

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Equilateral triangle

Question 45

In a triangle with sides of length a, b, and c, and semiperimeter s = (a + b + c) / 2, which formula calculates its area?

Accepted Answer

√s(s - a)(s - b)(s - c)

Answer

s * a * b * c

Answer

0.5 * base * height

Answer

π * radius²

Question 46

A triangle with two equal sides is termed as:

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Scalene

Answer

Right

Question 47

Which triangle type has three equal angles?

Accepted Answer

Equilateral

Answer

Acute

Answer

Obtuse

Answer

Right

Question 48

The Pythagorean theorem is expressed as:

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

a² + b² - c² = 0

Question 49

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

Accepted Answer

Opposite side

Answer

Adjacent side

Answer

Hypotenuse

Answer

Leg

Question 50

A triangle with angles measuring 45, 45, and 90 degrees is categorized as a:

Accepted Answer

Right triangle

Answer

Acute triangle

Answer

Obtuse triangle

Answer

Isosceles triangle

Question 51

Given a triangle with two sides measuring 5 cm and 7 cm, determine the acceptable range of values for the third side.

Accepted Answer

2 cm - 10 cm

Answer

2 cm - 12 cm

Answer

0 cm - 12 cm

Answer

0 cm - 10 cm

Question 52

Which property is NOT characteristic of similar triangles?

Accepted Answer

Perimeters are equal

Answer

Corresponding angles are equal

Answer

Corresponding sides are proportional

Answer

Areas are proportionate

Question 53

If two triangles have congruent corresponding angles, they are:

Accepted Answer

Congruent

Answer

Similar

Answer

Isosceles

Answer

Right

Question 54

A triangle with two equal sides is classified as:

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Answer

Right

Question 55

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

Accepted Answer

Right triangle

Answer

Equilateral triangle

Answer

Obtuse triangle

Answer

Acute triangle

Question 56

The formula to calculate the area of a triangle is:

Accepted Answer

A = ½ * b * h

Answer

A = b * h

Answer

A = l * w

Answer

A = πr²

Question 57

State the Pythagorean theorem:

Accepted Answer

a² + b² = c²

Answer

c² - a² = b²

Answer

a² - b² = c²

Answer

a² + b² + c² = 180

Question 58

For similar triangles, the ratio of the lengths of their corresponding sides is:

Accepted Answer

Equal

Answer

Supplementary

Answer

Complementary

Answer

Inversely proportional

Question 59

Which of the following is a criterion for angle classification in triangles?

Accepted Answer

Measure of the largest angle

Answer

Measure of the longest side

Answer

Measure of the smallest side

Answer

Area of the triangle

Question 60

A triangle with sides measuring 7 cm, 7 cm, and 9 cm is:

Accepted Answer

Isosceles

Answer

Scalene

Answer

Equilateral

Question 61

Calculate the perimeter of a triangle with side lengths a = 5, b = 7, and c = 9.

Accepted Answer

21 cm

Answer

14 cm

Answer

28 cm

Question 62

Which of the following triangles has the smallest area?

Accepted Answer

Triangle with base 4 cm and height 3 cm

Answer

Triangle with base 7 cm and height 6 cm

Answer

Triangle with base 5 cm and height 4 cm

Answer

Triangle with base 6 cm and height 5 cm

Question 63

Which type of triangle has three congruent sides?

Accepted Answer

Equilateral

Answer

Scalene

Answer

Isosceles

Answer

Right

Question 64

A triangle with two equal sides is classified as...

Accepted Answer

Isosceles

Answer

Equilateral

Answer

Right

Answer

Scalene