Your teacher will grade your responses for questions 13–15, to ensure that you receive proper credit for your answers.
Write a paragraph proof.
Given: modifying above B C with bar congruent to modifying above E C with bar and Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar
Prove: modifying above upper B upper A with barcongruent to Modifying above Upper E Upper D with bar
Segment B A is shown on the left. Segment D E is shown on the right. Segment B E intersects Segment A D at point C.
(5 points)
To prove that modifying above upper B upper A with bar is congruent to Modifying above Upper E Upper D with bar, we will use the Segment Addition Postulate and the Given information.
1. Given: modifying above B C with bar congruent to modifying above E C with bar and Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar
2. By the Segment Addition Postulate, we know that modifying above B C with bar + Modifying above upper A upper C with bar = modifying above upper B upper A with bar
3. By substitution, we know that modifying above E C with bar + Modifying above upper D upper C with bar = Modifying above Upper E Upper D with bar
4. Since modifying above B C with bar congruent to modifying above E C with bar and Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar, we can substitute these congruences into our equations
5. This gives us modifying above B C with bar + Modifying above upper A upper C with bar = modifying above upper B upper A with bar is congruent to modifying above E C with bar + Modifying above upper D upper C with bar = Modifying above Upper E Upper D with bar
6. Therefore, by the Transitive Property of Congruence, we can conclude that modifying above upper B upper A with bar is congruent to Modifying above Upper E Upper D with bar.
Thus, we have proven that modifying above upper B upper A with bar is congruent to Modifying above Upper E Upper D with bar.