Question

Answer: Proved QN = QR

Step-by-step explanation:

Given : In ║gm PQRS, SM =SR

To prove QN =QR

Proof :

In Δ SMR

∵ SM = SR

∠SMR =∠SRM

( Angles opposite to equal sides are equal)

Let ∠SMR =∠SRM = X...(1)

As,∠PSR is an exterior angle of ΔSMR

So, ∠PSR = ∠SMR +∠SRM

∠PSR = x + x= 2x....(2)

Since ∠PSR =∠PQR (Opposite angles of parallelogram PQRS)

So, ∠PQR = 2x...(3)

As PM║ QR

So, ∠PSR +∠QRS = 180

2x + ∠QRS = 180

∠QRS = 180 - 2x....(4)

As, ∠QRS +∠SRM +∠QRN =180

(180-2x) + x+ ∠QRN = 180 ( from 1 and 4)

(180 - x) + ∠QRN = 180

∠QRN = x ....(5)

Also, ∠PQR is an exterior angle of Δ QRM

So, ∠PQR =∠QRN +∠QNR

2x = x + ∠QNR (from 5 and 3 )

∠QNR = x....(6)

In Δ QNR,

∠QRN =∠ QNR

(from 5 and 6)

∴ QR = QN ( Angles opposite to sides are equal)

Answer 1

Answer:

this is the answer of prove thatQN = QR right

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