Question

In the given figure, $$PQ || BA$$ and $$RS\ CA$$. If $$BP=RC$$, prove that :
$$\triangle BSR \cong \triangle PQC$$

Answer 1

$$PQ || BA, RS || CA$$
$$BP = RC$$
To prove:
(i) $$\triangle BSR \cong \triangle PQC$$
(ii) $$RS=CQ$$
Proof: $$BP =RC$$
$$BC -RC=BC-BP$$
$$BR=PC$$
Now, in $$\triangle BSR $$ and $$\triangle PQC$$
$$\angle B =\angle P$$ (Corresponding angles)
$$\angle R =\angle C$$ (Corresponding angles)
$$BR =PC$$ (Proved)
$$\triangle BSR \cong \triangle PQC$$
$$BS=PQ$$
$$RS=CQ$$