Question

In triangle ABC angle bisector AE is equal to EC. Given AC=2·AB, find m∠ABC, in degrees.

Answer 1

m∠ABC = 90°

Explanation:

Given that AE = EC, triangle AEC is isosceles. Then the altitude from E to AC at D will be the perpendicular bisector of AC.

We know that AC = 2·AB, so AD = AC/2 = AB. Now, we can show triangles AED and AEB are congruent by SAS, so ...

m∠ABC = m∠ADC = 90°