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.
Proof:
Given: Segment BC ≅ Segment EC and Segment AC ≅ Segment DC
To prove: Segment BA ≅ Segment ED
Proof:
Since Segment BC ≅ Segment EC and Segment AC ≅ Segment DC, we can conclude that triangle BAC ≅ triangle EDC by Side-Side-Side (SSS) congruence.
Therefore, angle BCA ≅ angle ECD (corresponding angles of congruent triangles).
Since angle BCA + angle BAE = 180 degrees (because they form a straight line), and angle ECD + angle EDA = 180 degrees (also a straight line),
we can deduce that angle BAE ≅ angle EDA (subtracting angle BCA and angle ECD from both sides).
Thus, triangle BAE ≅ triangle EDA by Angle-Side-Angle (ASA) congruence.
As a result, segment BA ≅ segment ED (by corresponding sides of congruent triangles).
Therefore, Segment BA ≅ Segment ED, as required to be proved.