Given: BC is congruent to EC (modifying above BC with bar congruent to modifying above EC with bar) and AC is congruent to DC (modifying above AC with bar congruent to modifying above DC with bar)
To Prove: BA is congruent to ED (modifying above BA with bar congruent to modifying above ED with bar)
Proof:
1. Draw the line segment BA on the left and the line segment ED on the right.
2. Draw the line segment BC and EC, and mark the intersection point as C.
3. From the given, we know that BC is congruent to EC (modifying above BC with bar congruent to modifying above EC with bar) and AC is congruent to DC (modifying above AC with bar congruent to modifying above DC with bar).
4. By the transitive property of congruence, if BC is congruent to EC and AC is congruent to DC, then BC is congruent to DC.
5. We can conclude that triangle BAC is congruent to triangle EDC by the Side-Side-Side congruence criterion.
6. By the corresponding parts of congruent triangles, we can say that BA is congruent to ED (modifying above BA with bar congruent to modifying above ED with bar).
Therefore, BA is congruent to ED.
Short Answer
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.
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