Question

In the figure, give below, 2AD = AB, P is mid-point of AB, Q is mid-point of DR and PR // BS. Prove that:
(i) AQ // BS
(ii) DS = 3 Rs.

Answer 1

Given that AD = AP = PB as 2AD = AB and p is the midpoint of AB

(i) From triangle DPR, A and Q are the mid-point of DP and DR.
Therefore AQ || PR
Since PR || BS ,hence AQ || BS

(ii) From triangle ABC, P is the midpoint and PR || BS
Therefore R is the mid-point of BC

From ΔBRS and ΔQRC
∠BRS = ∠QRC
BR = RC
∠RBS + ∠RCQ
∴ ΔBRS ≅ ΔQRC
∴ QR =RS
DS = DQ + QR + RS = QR + QR + RS = 3RS