Question

q2...............................

Answer 1

Given:
2AD = AB
P is mid point of AB
Q is mid point of DR
PR || BS

To Prove: (1) AQ || BS (2) DS = 3RS

Proof:
2AD = AB
$ad = \frac{1}{2} ab$
AD = AP
A is mid point of DP

In ∆ DPR,
A is mid point of DP
Q is mid point of DR

By mid point theorem:
AQ || PR
PR || BS

Hence,
AQ || BS [ Proved (1) ]

AQ || PR || BS
DB & DS are transversals such that,
DA = QR = PB

By intercept theorem:
DQ = QR = RS

DS = 3RS [ Proved (2) ]


Hope it helps you my friend!!