Question

ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B. Prove that: (i)AQ=BP (ii)PQ=CD (iii)ABPQ is a parallelogram

Answer 1

Answer:

Step-by-step explanation:

Let

= 180 - (180 - x)

= 180 - 180 + x

= x

In

or AB = BP """"(1)

Now,

= 90 - x  

So,

and  (Alternate Interior Angles)

hence, AB = AQ """(2)

From equations (1) & (2) we get-

(i) AQ = PB Proved !

(iii) Since, AQ = BP &  (As ABCD is Parallelogram)

(Opposiote sides are equal & parallel, So, ABPQ is a parallelogram)

(ii) AB = PQ (As  ABPQ is a parallelogram)

and AB = CD (As  ABCD is a parallelogram)

Hence, CD = PQ (Proved)