CLASSIFYING TRIANGLES BASED ON SIDE MEASURES

On the basis of the length of the sides, triangles are classified into three categories.

• Scalene Triangle
• Isosceles Triangle
• Equilateral Triangle

Identify each triangle based on sides.

Problem 1 :

Solution :

By observing the figure, 

AB = BC = AC = 2yd

Since all the sides are equal in length, it is an

Equilateral Triangle

Problem 2 :

Solution :

By observing the figure, 

AB = 7 in, BC = 5 in, and, AC = 3 in

Since all the sides are different in length, it is an

Scalene Triangle

Problem 3 :

Solution :

By observing the figure, 

AB = 5 ft, BC = 3 ft, and, AC = 3 ft

Since the two sides are the same in length, it is an

Isosceles Triangle

Problem 4 :

Solution :

By observing the figure, 

AB = 3 in, BC = 2 in, and, AC = 2 in

Since the two sides are the same in length, it is an

Isosceles Triangle

Problem 5 :

Solution :

By observing the figure, 

AB = BC = AC = 4 ft

Since all the sides are equal in length, it is an

Equilateral Triangle

Problem 6 :

Solution :

By observing the figure, 

AB = 7 yd, BC = 9 yd, and, AC = 8 yd

Since all the sides are different in length, it is an

Scalene Triangle

Problem 7 :

Find the value of x. Then classify each triangle.

a. Flag of Jamaica

b. Flag of Cuba

Solution :

a)  Flag of Jamica :

Sum of interior angles of triangle = 180

128 + x + x = 180

128 + 2x = 180

2x = 180 - 128

2x = 52

x = 52/2

x = 26

The angle measures are 26, 26 and 128. Since two angle measures are equal, then it is isosceles triangle.

b) Flag of Cuba

x + x + 60 = 180

2x + 60 = 180

2x = 180 - 60

2x = 120

x = 120/2

x = 60

The angle measures are 60, 60, and 60. Since all angle measures are equal, then it is equilateral triangle.

Problem 8 :

An airplane leaves from Miami and travels around the Bermuda Triangle. What is the value of x?

a) 26.8      b) 27.2     c) 54      d) 64

Solution :

The angles are x, 62.8 and 63.2

Sum of interior angles = 180

x + 62.8 + 63.2 = 180

x + 126 = 180

x = 180 - 126

x = 54

Since the angle measures are different, then it must be scalene triangle.

Problem 9 :

Shown below is an isosceles triangle.

Work out the size of the angle marked y.

Solution :

y + 77 + 77 = 180

y + 154 = 180

y = 180 - 154

y = 26

So, the missing angle measure is 26. Since the two angle measures are equal, it must be a isosceles triangle.

Problem 10 :

In an acute triangle, the measures of two angles are 50° and 60°. What is the measure of the third angle?

Solution :

Two angle measures are 50° and 60°. Let x be the third angle.

x + 50 + 60 = 180

x + 110 = 180

x = 180 - 110

x = 70

So, the third angle measure is 70 degree.

Problem 11 :

In an obtuse triangle, the measures of two angles are 120° and 10°. What is the measure of the third angle?

Solution :

Two angle measures are 120° and 10°. Let x be the third angle.

x + 120 + 10 = 180

x + 130 = 180

x = 180 - 130

x = 50

So, the third angle measure is 50 degree.

Problem 12 :

One acute angle of a right triangle measures 35°. What is the measure of the other acute angle?

Solution :

Given that is a right triangle. The two angle measures are 90° and 35°. Let x be the third angle.

x + 90 + 35 = 180

x + 125 = 180

x = 180 - 125

x = 55

So, the other acute angle is 55.

Problem 13 :

In a triangle ABC, ∠A = 2X + 7, ∠B = 5X - 15, and ∠C = 6X. What is the value of x and what are the measures of angles A, B, and C?

Solution :

∠A + ∠B + ∠C = 180

2x + 7 + 5x - 15 + 6x = 180

2x + 5x + 6x + 7 - 15 = 180

13x - 8 = 180

13x = 180 + 8

13x = 188

x = 188/13

x = 14.4

So, the angle measures are 35.8, 57 and 86.4

Problem 14 :

Below are 3 straight lines.

Below are 3 straight lines.

Solution :

Let x be the missing angle inside the triangle.

151 + x = 180

x = 180 - 151

x = 29

y = 180 - (93 + 29)

y = 180 - 122

y = 58

So, the value of y is 58.