Question

The proof that ΔACB ≅ ΔECD is shown. Given: AE and DB bisect each other at C. Prove: ΔACB ≅ ΔECD What is the missing statement in the proof? ∠BAC ≅ ∠DEC ∠ACD ≅ ∠ECB ∠ACB ≅ ∠ECD ∠BCA ≅ ∠DCA

Answer 1

Answer with explanation:

Given: It is given that , in ΔACB and ΔE CD , A E and DB bisect each other at C.

To Prove: ΔA CB ≅ ΔE CD

Proof: In ΔA CB ,and ΔE CD

A E and DB bisect each other at C.

AC=CE -------[Given]

BC=CD-----[Given]

∠A CB = ∠E CD →→[Vertically opposite angles]

→∠A CB ≅ ∠E CD ⇒⇒[S A S]

Option C: →→∠A CB ≅ ∠E CD -------[missing statement in the proof]

Answer 2

The missing statement is ∠ACB ≅ ∠ECD

Explanation:

Given two lines segment AC and BD bisect each other at C.

We have to prove that ΔACB ≅ ΔECD

In triangle ACB and ECD

AC=CE (Given)

BC=CD (Given)

Now to prove above two triangles congruent we need one more side or angle

so, as seen in options the angle ∠ACB ≅ ∠ECD due to vertically opposite angles

hence, the missing statement is ∠ACB ≅ ∠ECD