Chapter 8: Similar Triangles

Example 4. Prove that any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally (i.e. in the same ratio)

Solution:-

Given:- PQRS is a trapezium in which PQ || SR || XY

To Prove:-

Construction:- PR is joined which intersects XY at A.

Proof:- In

[ Thales Theorem]

( Taking reciprocals)

From (i) and (ii) we get

Example 5. In the given figure DE || AQ and DF || AR

Prove that EF || QR

Solution:-

In

from (1) and (2) we get