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 Apr 20, 2020
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Since "ABC is an isosceles triangle with BA=BC" 

Therefore, angle BAD= angle BCA  (Let it be y) (1)

"D lies on AC, ABD is an isosceles triangle with AB=AD" 

AB=AD means that angle ABD= angle ADB = 72 degrees. (since ABD=72 (given)) 

so we can find y now.

in a triangle, the sum of angles is equal to 180 degrees.

Then, 180=72+72+y, y=180-144=36

we have found y and from (1) we conclude that also angle BCA= 36 degrees.

 

Since angle on straight line = 180 

Straight-line ADC have angle BDA=72, so the other angle BDC=180-72=108

In triangle BCD, since it is a triangle, angles add up to 180

then angle CBD= 180-108-36=36 as well. 

So angle DBC= angle DCB

Therefore, DB=DC

 Apr 20, 2020

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