Please Help Me On This Math Problem!!?
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!!!
Favorite Answer
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
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
