Please help with geometry triangle proof problem

[Gearhead14]

Given:Isosceles triangle AFC
with base line AC.

Isosceles triangle BGD
with base line BD.

Isosceles triangle BHC
with base line BC.

Prove: Triangle AED
is isosceles

I can't even figure out where to start with this problem.

 

[m_a_t_h]

Since triangle AFC is an isosceles triangle, angle 1= angle 3;

Also triangle BGD is an isosceles triangle, angle 2= angle 4;

Triangle HBC is an isosceles triangle, angle 2 = angle 3; which makes angle 1 = angle 4.

 

[Gearhead14]

Since triangle AFC is an isosceles triangle, angle 1= angle 3;

Also triangle BGD is an isosceles triangle, angle 2= angle 4;

Triangle HBC is an isosceles triangle, angle 2 = angle 3; which makes angle 1 = angle 4.

How does that make angle 1= to angle 4?

 

[Gearhead14]

Figured it out. You didn't mention the part about how you figured out that the angles were congruent. I realized that you left out the definition of an isosceles triangle, the theorem that states "If two sides of a triangle are congruent then their angles opposite the sides are congruent". You also left out the use of the transitive law and the theorem that states "If two angles are congruent, then the sides opposite are congruent." Thanks for the jump start but you need to work on how you give your advice.

 

[mmm4444bot]

Thanks for the jump start but you need to work on how you give your advice.

Hello Gearhead:

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