Class 10 Maths · Triangles · NCERT Exercise 6.4 · Question 4

Triangles Medium

In Fig. 6.17, if PQRS is a parallelogram and

A B ∥ P S

, then prove that

O C ∥ S R

Fig. 6.17

Answer

Proved: the similar triangles

△ O P S \sim △ O A B

and

△ C QR \sim △ C A B

, together with

P S = QR

, give

\frac{O S}{O B} = \frac{C R}{C B}

; hence

\frac{B S}{S O} = \frac{B R}{R C}

, and by the converse of BPT in

△ B O C

O C ∥ S R

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