Question

in parallelogram PQRS the line passing through point P intersects side QR at M and the extended side SR at N ,then prove that QM×SN=PS×SR​

Answer 1

Answer:

beacuse parallel line in a parallelogram so QM×SN=PS×SR

Answer 2

$QM \times SN = PS \times SR$ Proved.

Step-by-step explanation:

See the diagram attached.

Now, Δ PNS and Δ MNS are similar as PQRS is a parallelogram and PS ║ RM. {By Angle-Angle-Angle criteria}

So, we can write $\frac{RN}{SN} = \frac{MR}{PS}$

⇒ $\frac{SN - SR}{SN} = \frac{QR - QM}{PS}$

⇒ $1 - \frac{SR}{SN} = \frac{PS - QM}{PS}$ {Since PQRS is a parallelogram and QR = PS}

⇒ $1 - \frac{SR}{SN} = 1 - \frac{QM}{PS}$

⇒ $\frac{SR}{SN} = \frac{QM}{PS}$

⇒ $QM \times SN = PS \times SR$ Proved.