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
tonyas proof

statement	justification
2. ∠akl ≅ ∠gkb	2. vertical angles theorem
3. ∠gkb ≅ ∠flk	3. corresponding angles theorem
4. ∠akl ≅ ∠flk	4. transitive property

pearls proof

statement	justification
2. ∠akl ≅ ∠gkb	2. definition of adjacent angles
3. ∠gkb ≅ ∠flk	3. corresponding angles theorem
4. ∠akl ≅ ∠flk	4. transitive property

Explanation:

Pearl made an error. In step 2 of her proof, $\angle AKL$ and $\angle GKB$ are vertical - angles, not adjacent angles as she claimed. The vertical - angles theorem should be used instead of the definition of adjacent angles.

Answer:

Pearl completed the proof incorrectly because she misidentified $\angle AKL$ and $\angle GKB$ as adjacent angles instead of vertical angles in step 2 of her proof.