Question

( WILL GIVE BRAINLY) (20 POINTS) Tonya and Pearl each completed a separate proof to show that alternate interior angles AKL and FLK are congruent. Who completed the proof incorrectly? Explain. (10 points)
Tonya's Proof

Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKL is congruent to angle GKB 2. Vertical Angles Theorem
3. angle GKB is congruent to angle FLK 3. Corresponding Angles Theorem
4. angle AKL is congruent to angle FLK 4. Transitive Property


Pearl's Proof

Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKL is congruent to angle GKB 2. Definition of Adjacent Angles
3. angle GKB is congruent to angle FLK 3. Corresponding Angles Theorem
4. angle AKL is congruent to angle FLK 4. Transitive Property

Answer 1

Pearl's Proof is incorrect.

The theorem is to proof ∠AKL≅ ∠FLK.

The real proof is as follows:

• Line AB ║ EF with transversal segment Gj
• Angle AKL is congruent to angle GKB . (Vertical Angles Theorem)
• Angle GKB is congruent to angle FLK (Corresponding Angles Theorem)
• angle AKL is congruent to angle FLK (Transitive Property)

Therefore, Tonya's Proof is definitely right and Pearl's Proof is definitely wrong.

The second proof of pearl was wrong. Angle AKL is congruent to angle GKB but they are not adjacent angles.

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