Question

ABCD is a rhombus and P,Q,R,S are mid-points of AB,BC,CD,and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Answer 1

Answer:

pqrs is a rectangle

Step-by-step explanation:

Given:- In rhombus ABCD

P,Q,R and S are the mid points

of AB=BC=CD=DA.

To prove:- PQRS is a rectangle.

Proof:- In ∆ABD,

P and S are the mid points of

AB And AD as respectively.

Therefore, PS ll BD and PS =  (by the mid point theorem)----1.

In ∆CBD

Q and R are the mid points of

BC and CD respectively.

Therefore, QRllBD and QR=  BD. (by the mid point theorem)---- 2.

From 1 and 2

Therefore, PS ll QR and PS =QR

Therefore, PQRS IS A RECTANgle

Answer 2

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