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.
Drag an expression or phrase to each box to complete the proof.
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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
How to prove transitive property of Congruence?