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In triangle ABC, AB = AC, and angle A is equal to 36 degrees. Point D is on AC so that BD bisects angle ABC. 

(a) Prove that BC = BD = AD.

 

I just need some hints on this part a... I'm feeling a bit stuck.

 

Past Question: https://web2.0calc.com/questions/help_80380

The link given didn't really give much for a.

 Mar 24, 2021
 #1
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Since  AB = AC, the  angles  ABC = ACB  = 72°

 

Bisecting  angle  ABC  means that  angle  ABD =  angle BAD  = 36°

Therefore....in triangle   ABD......AD = BD

 

And the  thitd  angle in this triangle, BDA  =  108°

So angle  BDC   =  180  - 108°  =  72°

And  angle  ACB =  DCB = 72°

 

So.....in triangle  BDC, angle  DCB = angle BDC    

So  BD = BC

 

So

 

BC =  BD  = AD

 

cool cool cool

 Mar 24, 2021

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