Question

Show that the bisectors of the angles of a ||gm encloses a rectangle.

Wrong, copied and irrelevant answers will be deleted.​

Answer 1

Step-by-step explanation:

Explanation:-

Let ABCD be a parallelogram.

Let AS, BS, CQ and DQ be the bisectors of ∠A, ∠B, ∠C and ∠D respectively.

Since DC || AB and DA cuts them, we have,

∠A+∠D=180° (co-interior angles)

↠1/∠A+1/∠D=180°

↠∠PAD+∠ADP=90°

But, ∠PAD+∠ADP+∠APD=180°

90°+∠APD=180°

∠APD=180-90=90°

Now, ∠SPQ=∠APD=90°

Similarly, ∠PQR=90°, ∠QRS=90° and ∠PSR=90°

Thus, PQRS is a quadrilateral whose each of the angles is 90°

Hence, PQRS is a rectangle.