Question

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.

Answer 1

Given the image, we are asked to show who completed the proof incorrectly. To do this, we will take a look at pearl's proof and Tonya's proof.

Explanation

In the proof, we can see that the difference between Tonya and Pearl's proof lies in proof 2. For Pearl we have;

$\angle AKL\cong GKB(Adjacent\text{ angles)}$

For Tonya we have;

$\angle AKL\cong GKB(\text{Vertical angles)}$

Therefore, let's look at the definition of vertical angles and adjacent angles.

Definition

Vertical angles: Vertical angles are a pair of opposite angles formed by intersecting lines.

Adjacent angles: Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.

If we then look at the relationship between vertical angles.

Hence the wrong proof would be

Answer: Pearl's proof