Question

The proof that ΔACB ≅ ΔECD is shown.

Given: AE and DB bisect each other at C.
Prove: ΔACB ≅ ΔECD

Triangles A B C and C D E share common point C.

A flow chart has 5 boxes with arrows facing downward connecting the boxes. Each of the boxes are labeled. Box 1 contains line segment A E and line segment B E bisect each other at C and is labeled given. Box 2 contains line segment A C is-congruent-to line segment E C and is labeled definition of bisector. Box 3 contains question mark and is labeled vertical angles theorem. Box 4 contains line segment D C is-congruent-to line segment B C and is labeled definition of bisector. Box 5 contains triangle A C B is-congruent-to triangle E C D and is labeled SAS.

What is the missing statement in the proof?

∠BAC ≅ ∠DEC
∠ACD ≅ ∠ECB
∠ACB ≅ ∠ECD
∠BCA ≅ ∠DCA

Answer 1

∠ACB ≅ ∠ECD

Reason: AE and BD intersect at C, so the vertical angles ∠ACB and ∠ECD are congruent. This gives the included-angle needed for SAS with AC ≅ EC and BC ≅ DC.