Math CentralQuandaries & Queries


Question from Lisa, a student:

I am stuck on this problem... If AB = CD (parellel line), and <ACD = <ECD. I need to prove that the triangle ABC is isosceles. I cannot draw from my computer therefore if you need more details let me know.

Lias continued.

I was able to take a pic with my web cam so you'll get full details on the pic since I don't know how to draw you the pic.


Hi Lisa.

1. Corresponding angles formed by a transverse line crossing two parallel lines are congruent, therefore angle CAB equals angle ACD and that's x in your diagram.

2. For similar reasons, angle ABC equals angle DCE and that's also x.

The final step is connected to another problem you sent us.

Question from Lisa, a student:

This is a fill in the blanks that I just do not understand.

The (blank) angle of a triangle is equal to the sum of the (blank) opposite angles.

Can you formalize this and complete the proof?

Stephen and Penny

PS: Your web camera really helped!


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