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.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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


  1. Place the answers in this order
    CE =AC
    transitive property of congruence
    definition of isosceles triangle
    I included a link with proof  that these are the correct answers, I took the test.


  2. The conjecture and the two-column proof used to prove the conjecture are as explained below.

    How to prove transitive property of Congruence?

    Transitive property of congruence states that if one pair of lines or angles or triangles are congruent to 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.
    The two column proof to prove the given conjecture are as follow;
    Statement 1: S is the midpoint of RT        
    Reason 1: Given
    Statement 2: RS ≅ ST                              
    Reason 2: Definition of midpoint
    Statement 3: ST ≅ XY                              
    Reason 3: Given
    Statement 4:  RS ≅ XY                              
    Reason 4: Transitive property of congruence
    Read more about Transitive property of congruence at;


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