**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.2 Question 10**

**10. The diagonals of a quadrilateral ABCD intersect each other at the point O such that . Show that ABCD is a trapezium.**

**Solution:**

**Given: **

** (1)**

**To Prove: **ABCD is a trapezium or AB CD.

**Construction: **Draw line EO to AB touching BC at F.

**Proof:**

In ABD, EO AB.

Therefore, by **Basic Proportionality Theorem,** we get

** (2)**

From** (1)** and **(2)**, we get

Therefore, by **Converse of Basic Proportionality theorem**, we get

EO DC. **(3)**

But, we also have EO AB ** (By construction) (4)**

**Therefore, from (3) and (4), we have AB DC which means ABCD is a trapezium.**

**Hence Proved.**