Question

17. Write a two-column proof to prove these two triangles are congruent:

Given: BC is congruent to CD, and AC is congruent to CE

Prove:Triangle ABC is congruent to Triangle EDC​

Answer 1

A two-column proof demonstrates that triangle ABC is congruent to triangle EDC by using the given equalities of BC ≅ CD and AC ≅ CE, and applying the Isosceles Triangle Theorem and SAS Postulate.

Step-by-step explanation:

Two-Column Proof for Congruent Triangles

To prove that triangle ABC is congruent to triangle EDC given that BC is congruent to CD, and AC is congruent to CE, we can use a two-column proof format. Here it is, step-by-step:

1. Given: BC ≅ CD, AC ≅ CE
2. Prove: △ABC ≅ △EDC
3. Statement: BC ≅ CD (given)
4. Reason: Given
5. Statement: AC ≅ CE (given)
6. Reason: Given
7. Statement: Angle B ≅ Angle D
8. Reason: Angles opposite to equal sides are equal (Isosceles Triangle Theorem)
9. Statement: △ABC ≅ △EDC
10. Reason: SAS Postulate (Side-Angle-Side)

By establishing the congruence of two sides and the included angle, we have proven that the two triangles are congruent according to the SAS Postulate.