**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.2 Question 9**

**9. ABCD is a trapezium in which AB DC and its diagonals intersects each other at the point O. Show that **

**Given:**AB DC in trapezium ABCD.

**To Prove:**

**Construction: **Draw line EF passing through O parallel to AB. A line parallel to AB is also parallel to DC.

**Proof: **In ADC, EO DC.

Therefore, by **Basic Proportionality Theorem**, we get ** (1)**

In ABD, EO AB.

Therefore, by **Basic Proportionality Theorem**, we get **(2)**

Therefore, from **(1)** and **(2), **we get

**Hence Proved**