Question

From the given figure, prove that (i) BX AP 2 (ii) AP + CR

Answer 1

Answer:

The given figure is a trapezium are the points B and Q mid points of their respective sides.

We know that sum of parallel sides is equal to twice of the line joining the mid points of non parallel sides.

You can use the mid point theorem and its converse for solving the question.

In triangle ACP,

X is mid point of PC [converse of mid point theorem]

Also BX =1/2 AP [mid point theorem].(1)

Similarly by using both theorems in triangle CRP,

We can prove

XQ = 1/2 CR .(2)

(1) + (2) = BX + XQ

= 1/2(AP + CR)

This implies AP + CR = 2 BQ