Question

8. ABCD is a rectangle in which diagonal AC bisects 2 A as well as Z C. Show that:
(1) ABCD is a square (ii) diagonal BD bisects ZB as well as ZD,​

Answer 1

Answer:

Given;- -ABCD is a rectangle in which diagonal AC bisects angle A as well as angle C .

To prove :-1) ABCD is a square .

2)diagonal BD bisects angle B as well as angle d .

PROOF:-1)Since AC bisects angle A as well as angle C in the rectangle ABCD .

angle 1=angle 2 =angle 3 =angle 4 (each =90/2=45 degree)

In triangle ,angle 2 = angle 4

=AD=CD ( Sides opposite to equal angles)

Thus, the rectangle ABCD is a square .

2)In a square ,diagonals bisect the angles .

So, BD bisects angle B as well as angle D .