A conjecture and the two-column proof used to prove the conjecture are shown.

Given: segment A B is congruent to segment B D, segment B D is congruent to segment C E, and segment C E is congruent to segment A C. Prove: triangle A B C is an isosceles triangle. Segment A D with endpoints D and A moving from left to right. Segment A D is diagonally down to the left from point A. B is the midpoint of segment A D. Segment A E shares endpoint at point A with segment A D. Segment A E is diagonally down to the right from point A. C is the midpoint of segment A E. Segment B C is horizontal between segment A D and segment A E.

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Statement Reason

1. AB¯¯¯¯¯≅BD¯¯¯¯¯ Given

2. BD¯¯¯¯¯≅CE¯¯¯¯¯ Given

3. Response area Transitive Property of Congruence

4. Response area Given

5. AB¯¯¯¯¯≅AC¯¯¯¯¯ Response area

6. △ABC is an isosceles triangle. Response area

AB=CECE =ACtransitive property of congruencedefinition of isosceles triangletwo-column proofused to prove the conjecture are as explained below.## How to prove transitive property of Congruence?

Transitive propertyofcongruencestates that if one pair of lines or angles or triangles arecongruentto a third line or angle or triangle, then it means that the first line or angle or triangle is congruent to the third line or angle or triangle. For example, if ∠A is congruent to ∠ B, and ∠ B is congruent to ∠ C, then we can say that, ∠ A is congruent to ∠ C.two column proofto prove the givenconjectureare as follow;midpointof RTDefinition of midpointTransitive property of congruenceTransitive property of congruenceat; https://brainly.com/question/2416659