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 1. AD = BC, BC ⊥ AE, AD ⊥ BE Given 2. ∠D and ∠C are right angles CPCTE 3. ∠E = ∠E Reflexive 4. Triangle ADE congruent to Triangle BCE LA 5. ∠A = ∠B Perpendicular lines form right angles.

Answer 1

1. RM = SN, TM = TN Addition Property of Equality  

2. ∠T = ∠T Reflexive  

3. RM + TM = SN + TN Substitution  

4. RM + TM = RT, SN + TN = ST Betweeness  

5. RT = ST CPCTE  

6. Triangle RTN congruent to Triangle STM Given  

7. RN = SM SAS

Answer 2

Answer:

It is proved that ∠A = ∠B.

Step-by-step 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