7.5 Inequalities in Triangles

Key Formulas

Solved Examples

Step 1

In $\Delta ADC$ , $AD = AC$ (Given), so $\angle ADC = \angle ACD$ (Angles opp equal sides).

Step 2

$\angle ADC$ is an exterior angle for $\Delta ABD$ .

Step 3

Therefore, $\angle ADC > \angle ABD$ (Ext angle > Int opp angle).

Step 4

Substituting from step 1: $\angle ACD > \angle ABD$ , or $\angle C > \angle B$ .

Step 5

In $\Delta ABC$ , since $\angle C > \angle B$ , the side opposite $\angle C$ is longer than the side opposite $\angle B$ .

Step 6

Therefore, $AB > AC$ .

Step 7

Since $AC = AD$ , $AB > AD$ .

Final Answer

Proved.

Interactive Solver