Michael and Derrick each completed a separate proof to show that corresponding angles AKG and ELK are congruent. Who completed the proof incorrectly? Explain. Line AB is parallel to EF, transversal GJ crosses line AB at K and crosses line EF at L. Michael's Proof Statement Justification 1. line AB ∥ line EF with transversal segment GJ 1. Given 2. angle AKG is congruent to angle AKL 2. Vertical Angles Theorem 3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem 4. angle AKG is congruent to angle ELK 4. Transitive Property Derrick's Proof Statement Justification 1. line AB ∥ line EF with transversal segment GJ 1. Given 2. angle AKG is congruent to angle BKL 2. Vertical Angles Theorem 3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem 4. angle AKG is congruent to angle ELK 4. Transitive Property

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13-09-2022
Mathematics

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Michael and Derrick each completed a separate proof to show that corresponding angles AKG and ELK are congruent. Who completed the proof incorrectly? Explain. Line AB is parallel to EF, transversal GJ crosses line AB at K and crosses line EF at L. Michael's Proof Statement Justification 1. line AB ∥ line EF with transversal segment GJ 1. Given 2. angle AKG is congruent to angle AKL 2. Vertical Angles Theorem 3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem 4. angle AKG is congruent to angle ELK 4. Transitive Property Derrick's Proof Statement Justification 1. line AB ∥ line EF with transversal segment GJ 1. Given 2. angle AKG is congruent to angle BKL 2. Vertical Angles Theorem 3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem 4. angle AKG is congruent to angle ELK 4. Transitive Property

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bharathparasad577 bharathparasad577 · Answer 1 · 2022-09-17T23:35:40-04:00

Michael's proof is incorrect.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

We have AB is parallel to EF with transversal GF.

By vertical angles theorem, ∠ AKG ≅ ∠ BKL

By Alternate interior angles, ∠ BKL ≅ ∠ ELK

By the transitive property, ∠ AKG ≅ ∠ ELK

Now, Michael's completed the proof incorrectly.

In the second assertion, he makes the claim that the vertical angles theorem proves that AKG = AKL. However, the claim is untrue because AKG and AKL are angled on each side of a straight line GJ that is intersected by a tangent that is not perpendicular to GJ.

The angles AKG and AKL are forming a Linear pair. So Derrick's proof is right.

Learn more about angles here:

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