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scZoUnD [109]
3 years ago
11

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

Mathematics
1 answer:
Mice21 [21]3 years ago
8 0

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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