Mathematics
In the adjoining figure, PQ || BA and RS || CA. If BP = RC, prove that:
(i) △BSR ≅ △PQC
(ii) BS = PQ
(iii) RS = CQ.
Answer
Given, BP = RC
⇒ BR - PR = PC - PR
⇒ BR = PC.
Now, in △BSR and △PQC,
∠B = ∠P (Corresponding angles)
∠R = ∠C (Corresponding angles)
BR = PC (Proved)
Hence, proved △BSR ≅ △PQC by ASA axiom.
(ii) We know that corresponding parts of congruent triangles are equal.
∴ BS = PQ.
(iii) We know that corresponding parts of congruent triangles are equal.
∴ RS = CQ.
Related Questions
In the adjoining figure, AB = AC, D is a point in the interior of △ABC such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of △ABC.
In the adjoining figure, AB || DC. CE and DE bisects ∠BCD and ∠ADC respectively. Prove that AB = AD + BC.
In the adjoining figure, ABCD is a square. P, Q and R are points on the sides AB, BC and CD respectively such that AP = BQ = CR and ∠PQR = 90°. Prove that
(a) △PBQ ≅ △QCR
(b) PQ = QR
(c) ∠PRQ = 45°
In the adjoining figure, OA ⊥ OD, OC ⊥ OB, OD = OA and OB = OC. Prove that AB = CD.