SOLUTION: PROVE: An angle bisector of the vertex angle of an isosceles triangle is also an altitude. Thanks.

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Question 550468: PROVE: An angle bisector of the vertex angle of an isosceles triangle is also an altitude. Thanks.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Given: ᐃABC, 
       AB ≅ AC, 
       AD bisects ∠BAC 

To prove: AD ⊥ BC 
 
 

 Steps:                       Reasons:
1.   AB ≅ AC                  Why?
2. ∠ABD ≅ ∠ACD               Why?
3.   AD ≅ AD                  Why?
4. ᐃABD ≅ ᐃADC               Why?
5. ∠ADB ≅ ∠ACD               Why? 
6.  m∠ADB = m∠ACD = 90°      Two congruent angles that form a linear 
                              pair are right angles

7.   AD ⊥ AC                  Why?              
8.   AD is an altitude        Why?

I filled in the reason for step 6.  You fill in the reasons for the
other steps.  You could combine two of the steps.

Edwin