Question

Let P,Q,R,S as a mid point of side AB,BC,CD,DA of quadrilateral ABCD. Show that ABCD is a parallelogram.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

REF.Image.

In △ADC, by mid point

theorem, SR∥AC,SR= 1/2 AC

Similarly PQ∥AC,PQ= 1/2(AC)

PQ∥RS, similarly PS∥QR

⇒ opposite sides parallel

⇒PQRS is a parallelogram

As △ALS∼△AOD (AA similarity)

⇒ SL/ OD = AS/AD = 1/2

⇒ Area of rectangle = SL × R

= SL ×R = 1/2 (OD) (AC/2 )

{ LX x = SR = AC/2 }

= 1/2 (ar△ACD) + 1/2 (arACB)

= 1/2 ( arABCD)

Step-by-step explanation:

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