Question

Match the following STATEMENTS to the reasons listed.

NOTE: In a traditional proof format, the statements would be on the left side of the proof.

Given:
AD = BC


Prove:
A = B

Answer 1

It is proved that ∠A = ∠B.

Explanation:

1. Given: AD=BC, BC⊥AE, AD⊥BE

2. Reflexive Property: ∠E = ∠E

3. LA: Triangle ADE congruent to Triangle BCE

4. Perpendicular lines form right angles: ∠D and ∠C are right angles.

5. CPCTE: ∠A = ∠B

Answer 2

Explanation:

1. AD = BC, BC⊥AE, AD⊥BE [3] Reflexive

2. ∠D and ∠C are right angles [4] LA

3. ∠E = ∠E [2] perpendicular lines from right

angles

4. Triangle ADE is congruent

to Triangle BCE [1] Given

5. ∠A = ∠B [5] CPCTE