Write a complete proof for the following.

Question

PICTURE: https://pasteboard.co/GWgMblg.png

Given: EC // AB in △ABD

Prove: ∠AEC > ∠B

Answer 1

I'll let you write out the formal proof but let's walk through the general steps and theorems you should use. 

 

First you can show that triangles (ABD and ECD) are similar using AAA. Angle D is congruent to Angle D by the reflexive property. Angle B is congruent to Angle C because these are corresponding angles formed by two parallel lines and a transversal. Angle A and Angle E are congruent for the same reason. 

 

Now, if you focus just on the inner triangle, you can see that angle AEC is the exterior angle to triangle ECD. The exterior angle theorem tells you that angle AEC is equal to angle C + angle D. By substitution we can also say that angle AEC is equal to angle B + D (since angle B is congruent to angle D). 

 

If angle AEC = angle B + angle D then angle AEC must be greater than angle B!