Answer with explanation:
To prove that , the diagonals of Parallelogram ,A B CD,Bisect each other
That is, 1. A O=OD
2. BO=O C
We need to prove ,that either of two triangles
1. ΔA OB ≅ Δ DOC
or
2. ΔA O C ≅ Δ DOB
We will prove ,ΔA OB ≅ Δ DOC , in the following way.
1.∠A OB ≅ ∠ DOC→→→[Vertically Opposite angles]
2. AB=CD →→→[Opposite sides of parallelogram]
3. ∠BAD=∠C DA→[As, AB║CD,so Alternate interior angles are equal.]
⇒ΔA OB ≅ Δ DOC→→→ [A A S]
So, A O=OD→→[C PCT]
and, CO=OD→→[C PCT]
Similarly,we can prove that, ΔA O C ≅ Δ DOB,and get
A O=OD
and, CO=OD
To prove that,diagonals bisect each other of a Parallelogram,we need to prove
D) A O≅OD
