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

Answers

  1. The statement that completes the proof is  ΔACB ≅ ΔECD.

    What is the statement in the proof?

    • Triangles that are congruent have the same size and shape as similar triangles, albeit their shapes may differ. ” is used to represent congruent triangles.
    • Congruent triangles are similar triangles.
    • The statement that completes the proof is  ΔACB ≅ ΔECD
    • From the complete question (see attachment), we have the following highlights
    AC ≅ CE
    BC ≅ CD.
    • The angle at point C of both triangles are congruent
    i.e.   ΔACB ≅ ΔECD
    • This means that the missing statement of the proof is that the angles at C of both triangles are congruent.
    • Hence, the statement that completes the proof is  ΔACB ≅ ΔECD.
    To Learn more About  completes the proof  refer to:
    #SPJ1

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