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

The student is attempting a geometric proof involving congruent triangles and congruent angles. After matching given statements to proper reasons, it's clear the proof uses perpendicular lines, the reflexive property, and the SAS Postulate to conclude that ∠A is congruent to ∠B.

Step-by-step explanation:

The student's question appears to concern geometric proof construction, specifically proving that two angles are congruent (∠A = ∠B) given the premise that side AD = BC and both are perpendicular to another line segment. The given and reasons listed are to be matched to demonstrate the steps involved in a proof. Let's correct and match the statements to their reasons:

1. AD = BC, BC ⊥ AE, AD ⊥ BE - Given
2. ∠D and ∠C are right angles - Definition of Perpendicular lines form right angles.
3. ∠E = ∠E - Reflexive Property of Equality.
4. Triangle ADE congruent to Triangle BCE - Side-Angle-Side (SAS) Postulate or LA (Leg-Angle), as two sides and the included angle are congruent.
5. ∠A = ∠B - Corresponding Parts of Congruent Triangles are Equal (CPCTE).

Each step in the proof builds upon previous information and associations from geometric theorems and definitions. The proof relies on understanding concepts such as the reflexive property, perpendicular line definitions, and congruence postulates.

Answer 2

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