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roxygal602

Please Help Me On This Math Problem!!?

Prove: If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle

Given: Triangle ABC is isosceles; Segment CD is the altitude to base segment AB

To Prove: Segment CD bisects angle ACB

Plan: ???? Need Help

Please Help me plan a proof with statements and reasons. I have the first statement and reason. Triangle ABC is isosceles; segment SD si the altitude to base segment AB.

The Reason is (Given)

Please help me!!!

Top 3 Answers
    

Favorite Answer

we know that in an isosceles triangle, there are (at least) 2 congruent sides.

1) Isosceles Δ ABC by given

2) CA = CB by defination of isosceles triangle

3) CD is the Perpenicular Bisector of segment AB by The Converse of Perpendicula Bisector Theorem

4) AD = DB by Midpoint Postulate

5) CD = CD by relexive property

6) Δ ACD = Δ BCD by SSS

7) < ACD = < BCD by CPCTC 8) Conclusion: CD bisects

0

rabid_dog
This is quite easy. Prove triangle ACD and triangle BCD congruent.

AC = BC (since ABC is isosceles)

ang CAD = ang CBD (since ABC is isosceles)

ang CDA = ang CDB (since CD is the altitude)

therefore triangle ACD is congruent to triangle BCD by angle-angle-side congruency theorem.

By the corressponding parts of the congruent triangle, AD = BD.

i.e. D is the midpoint of AB

i.e. CD bisects AB

0

K.Punk
This is tough…. If I had it on paper, I could help you better, but I don’t, so sorry.
0

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