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

Question 550468: PROVE: An angle bisector of the vertex angle of an isosceles triangle is also an altitude. Thanks.
Answer by Edwin McCravy(20056) (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

RELATED QUESTIONS
How do I prove that the angle bisector of the vertex angle of an isosceles triangle is an (answered by KMST)

How to write a 2 column proof to show that an angle bisector of the vertex of an... (answered by richard1234)

Conjecture: The angle bisector of the vertex angle of an isosceles triangle is also a... (answered by Edwin McCravy,ikleyn)

How do you prove the median from the vertex angle of an isos. triangle is also an angle... (answered by solver91311)

The altitude from the vertex angle of an isosceles triangle is ____?____ the median?... (answered by asuar010)

Given: Segment RV is an angle bisector. Segment RV is an altitude Prove:... (answered by ikleyn)

PROVE: If an isosceles triangle has an altitude from the vertex to the base, then the... (answered by vleith,gonzo)

If two sidesof a triangle are congruent, then the _________ opposite those sides are... (answered by Edwin McCravy)

If an angle bisector of a triangle is the perpendicular bisector of the opposite side,... (answered by richwmiller)