1. ## Thales' theorem

I could solve the first question but got stock in the second one. I have spent so many ours in solving the second one but with no luck. Please help.

The non parallel sides [QD] and [UA] of the trapezoid are cut by a line parallel to the bases in B and C respectively.
1) Show that QB/BD = UC/CA
using Thales' theorem:
QB/BD = QR/RA
UC/CA = QR/RA
Then, QB/BD = UC/CA

2) Find a ratio equal to BC/DA (SHOW YOUR WORK)

2. ## Re: Thales' theorem

NOT "showing my work", $\frac{BC}{DA}= \frac{QU}{BC}= \frac{QU}{DA}$. You give the reasons.

3. ## Re: Thales' theorem

Thank you for the hint.
I still don't know how you got this answer. I have tried to find the reason for your answer but couldn't. Please, help me.

However, this leads me to another question.
Using your answer QU/BC = QU/DA, does this mean BC/DA = 1 always?