Relationship between Sides and Angles of a Triangle

Relationship between Sides and Angles of a Triangle

How to solve the relationship between sides and angles of a triangle problems: examples and their solutions.

Example 1

Determine the relationship between the measures of angle A, B, and C for the given triangle. AB = 5, AC = 7, BC = 8

The larger angle lies opposite the longer side.

(blue side) > (green side) > (red side).

So m∠(blue) > m∠(green) > m∠(red).

Example 2

Determine the relationship between AB, AC and BC for the given triangle. The measure of angle A = 62, The measure of angle B = 52, The measure of angle C = 66

The longer side lies opposite the larger angle.

m∠(blue) > m∠(green) > m∠(red).

So (blue side) > (green side) > (red side).

Example 3

Determine the relationship between AB, AC and BC for the given triangle. The measure of angle A = 46, The measures of angle B and C = 67

The congruent angles lies opposite the congruent sides.
This is the property of an isosceles triangle.

(blue side) = (green side) > (red side).

So m∠(blue) = m∠(green) > m∠(red).