Classifying Triangles

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Triangles can be classified on the basis of two aspects, sides and angles. Triangles on the basis of sides are divided into three types: Equilateral triangle (in which all the sides are equal), Isosceles triangle (in which any two sides are equal), Scalene triangle (none of the sides are equal). Similarly, triangles on the basis of angles can be divided into three types: Acute triangle (each angle less than 90º), obtuse triangle (one angle greater than 90º), and right triangle (one angle measures 90 º).

Example 1: If the perimeter of the triangle ABC is 21m and length of two sides of the triangle is 7m each respectively, then triangle ABC is classified as which triangle?

Let the length of the third side be = x                                                                   A

Perimeter of a triangle = Sum of all the sides of the triangle

Then, Perimeter = x + 7 + 7 = 21

Therefore, x + 14 = 21 ==> x = 21 – 14 = 7                                         B                          C

This implies the length of the third side is also = 7m                                  

Since all the three sides of the triangle are equal in measure, hence triangle ABC is an equilateral triangle.

Example 2: In triangle PQR, measure of angle P and measure of angle R is 50º and 40º respectively. Triangle PQR is classified as which triangle?

Let the measure of angle Q be = x

Sum of all the angles in a triangle = 180º

Then, angle P + angle Q + angle R = 180º

Therefore, 50º + x + 40º = 180º ==> x + 90= 180º ==> x = 90º  Q                         R

This implies that angle Q = 90º

Since one of the angles in triangle PQR = 90º, hence triangle PQR is a right triangle.

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