Question

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i)ABCD is a square (ii) Diagonal BD bisects ∠B as well as ∠D.

Answer 1

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

◽To proove :-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 .

◽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 .

Answer 2

Plz refer to the pic given

Hope It Helps