Problem 5

Given: , , , and .

Prove: is parallel to .

[Problem submitted by Steve Lee, LACC Professor of Mathematics.]

Solution:

B

Extend to E, and

draw .

Therefore,

in and .

Without loss of generality, let .

Then .

. Therefore, is isosceles. So, .

. Therefore, . So, .

. Therefore, .

Therefore, is parallel to .