Question

Write a two column proof

Given: angle ABE is congruent to angle DBC
prove: angle ABC is congruent to angle DBE

Answer 1

Using a two-column proof and angle addition postulate, it has been shown that if angle ABE is congruent to angle DBC, angle ABC must be congruent to angle DBE.

Step-by-step explanation:

To prove that angle ABC is congruent to angle DBE, we will assume that the given information is that angle ABE is congruent to angle DBC. A two-column proof structure is used to show the logical progression of the proof.

1. Given: Angle ABE is congruent to angle DBC.
2. To Prove: Angle ABC is congruent to angle DBE.
3. Proof:
4. Angle ABE is congruent to angle DBC (Given).
5. Angle ABE + Angle EBC = Angle ABC (Angle Addition Postulate).
6. Angle DBC + Angle EBC = Angle DBE (Angle Addition Postulate).
7. Since Angle ABE is congruent to angle DBC, angles ABC and DBE have the same measure when Angle EBC is added to each (Congruence & Addition).
8. Therefore, Angle ABC is congruent to angle DBE (Congruence of angles).