Question

PQRS is a parallelogram M is a point on PQ produced. SM intersects QR at N. show that triangle NQM ~ triangle SPM​

Answer 1

Step-by-step explanation:

In △SMR,

⇒  SM=SR               [ Given ]

∴  ∠SMR=∠SRM         [ Angles opposite to equal sides are equal ]

Let ∠SMR=∠SRM=x     ----- ( 1 )

As ∠PSR is an exterior angle of △SMR

⇒  So, ∠PSR=∠SMR+∠SRM

⇒  ∠PSR=x+x=2x      ---- ( 2 )

⇒  ∠PSR=∠PQR       [ Opposite angles of parallelogram PQRS ]

⇒  So, ∠PQR=2x         ----- ( 3 )

As PM∥QR

⇒  So, ∠PSR+∠QRS=180o.

⇒  2x+∠QRS=180o.

⇒  ∠QRS=180o−2x              ----- ( 4 )

As, ∠QRS+∠SRM+∠QRN=180o

⇒  (180o−2x)+x+∠QRN=180o         [ From ( 1 ) and ( 4 ) ]

⇒  (180o−x)+∠QRN=180o

⇒  ∠QRN=x    ---- ( 5 )

Also, ∠PQR is an exterior angle of △QRM

So, ∠PQR=∠QRN+∠QNR

⇒  2x=x+

Answer 2

Step-by-step explanation:

MKS is a unit of measurement. MKS stands for Meter, Kilogram and second. ... CGS system stands for Centimeter- Gram- Second system. In CGS system, length is measured in centimeters mass is measured in grams and time is in seconds.