Question

4) In the adjoining figure, PQ || BA and RS II CA. If BP =
RC, prove that:
(i) triangleBSRis congruent to trianglePQC
(ii) BS = PQ
(iii) RS = CQ.
Pls answer these guys I will mark the best answer as the brainliest
Plsssss

Answer 1

Answer:

We have BP = RC

=> BP + PR = RC + PR

=> BR = PC

Now since PQ || BA then angleB = angleP

Similarly, angleR = angleC

Now, in ∆BSR & ∆PQC

angleB = angleP

BP = PC

angleR = angleC

i) Hence, by ASA congruency rule, ∆BSR congruent to ∆PQC

ii) Since, the two traingles are congruent, hence, the side along the triangles are also equal

Hence, BS = PQ

iii) And similarly, RS = CQ