Expert: Sherry Wallin - 8/12/2010

Question
Hi!
I hope you can help me answer this question:
I need to 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;CD is the altitude to base AB.
To Prove:CD bisects angle ACB
Plan: ?( I was not sure what the plan should be)
Can you please tell me how I can prove it?I thought I should use the Isosceles Triangle Theorem..?

I also needed help with this question:
Use an indirect proof to show that John exceeded the 55 mph speed limit if he left his house at 8:15 a.m. and arrived at his office 60 miles away at 9:00 a.m. Write the proof using the paragraph method?
Thanks a lot for helping me!

Answer
Sara~
   If you have an isosceles triangle then you have two congruent triangles. Please see the attached drawing.

Math Prof

Note: I used line segment BD as the altitude and I forgot to answer your second question:

Suppose John left his house at 8:15am and arrived at his office 60 miles away at 9am but traveled at less than 55mph. This means he covered 60 miles in 45 minutes or that he had to be traveling on the average 80 mph. The contradiction is that 80 mph is not less than 55 mph, therefore you can conclude that it isn't true what you assumed and it must be false that he was traveling less than 55mph.