Question

17.P is the mid-point of the side AB of a parallelogram ABCD.A line is through B parallel
to PD meets DC at Q and AD produced at R.Prove that
1. AR = 2BC
2. BR =2BQ
​

Answer 1

Solution :

1. In Triangle ARB, P is the mid point of AB &

PD|| BR

Hence, D is a mid point - point of AR

[ converse of mid-point theorem ]

AR = 2AD

But remember, BC =AD [opp sides of Gm ABCD]

Therefore, AR = 2BC

(proved)

2. ABCD is a parallelogram

That's why, we can write DC || AB => DQ ||AB

Now, in Triangle ARB, D is a mid point of AR & DQ|| AB

Hence, Q is a mid point of BR

=> BR = 2BQ

(proved)

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Answer 2

Answer:

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