PLEASE HELP Given that ABCD is a parallelogram, what must be proven to prove that the diagonals bisect each other?

A) ΔACD≅ΔABD
B) AB||CD
C) AD≅CB
D) AO≅OD

PLEASE EXPLAIN WHY AND CHOOSE FROM THE AWNSER CHOICES GIVEN

Question

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Respuesta :

Аноним Аноним · Answer 1 · 2019-05-17T10:32:13+02:00

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

MrRoyal MrRoyal · Answer 2 · 2022-02-08T14:07:04+01:00

The statement that must be proven to show that the diagonals bisect each other is (d) AO≅OD

From the figure, the diagonals are:

Line segments AD and BC

The point halfway both segments is point O

The diagonals of a parallelogram bisect each other.

This means that:

Hence, the statement that must be proven to show that the diagonals bisect each other is (d) AO≅OD