In triangle ABC angle bisector AE is equal to EC. Given AC=2·AB, find m∠ABC, in degrees.
1 answer:
Answer:
m∠ABC = 90°
Step-by-step 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°
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