SOLUTION: Hi I am having trouble with an isosceles proof. I have triangle ABC. AD is perpendicular to BC. I need to prove that triangle ABC is an isosceles triangle. Given: <

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Question 453114: Hi I am having trouble with an isosceles proof. I have triangle ABC. AD is perpendicular to BC. I need to prove that triangle ABC is an isosceles triangle.

Given:
< BAD is ~= (congruent) to < CAD
AD is perpendicular to BC
Prove:
triangle ABC is isosceles

I need statements and reasons to explain this.
Answer by pedjajov(51) (Show Source):
You can put this solution on YOUR website!
Isosceles triangle has two equal sides (legs) and third that we call base.
Angles that base forms with legs are equal (congruent).
:
In given triangle we have that height AD halves the angle in vertex A.
AD also forms two right triangles ABD and ACD.
:
In these two triangles we have
angle BAD = angle CAD, it is given
angle ADC = angle ADB, these two are right angles
:
Now remaining angles ACD and ABD have to be also equal.
:
Since these two angles are equal it makes BC a base and BA and CA legs of isosceles triangle.