ABCD is a quadrilateral with AB parallel to CD. A line drawn parallel to AB meets AD at P and BC at Q. Prove that .

Question

Philoid · Accepted Answer

Given: ABCD is a quadrilateral with AB parallel to CD and line drawn parallel to AB meets AD at P and BC at Q

Required: To prove

Construction: draw a diagonal AC, which intersects PQ at R

Now, in ΔABC

Here, QR||AB

∴ By Thales theorem

⇒ --eq(1)

Now, consider ΔACD

Here, RP||DC

∴ By Thales theorem --eq(2)

From --eq(1) and –eq(2)

We have,

∴

Hence Proved