What is the missing step in the proof?

A. Statement: ∠IKL≅∠JLK

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

B. Statement: ∠IKL and ∠IKC are supplementary.

Reason: Linear Pair Theorem

C. Statement: ∠GJI≅∠JLK

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

D. Statement: ∠GJI and ∠IJL are supplementary.

Reason: Linear Pair Theorem

1. ∠EIJ≅∠GJI given

2. ∠EIJ≅∠IKL For parallel lines cut by a transversal, corresponding angles are congruent.

3. ∠IKL≅∠GJI Transitive Property of Equality

4.

5. ∠IKL and ∠IJL are supplementary. Transitive Property of Equality

Question

Mathematics

Quinn Savage

8 February, 08:49

What is the missing step in the proof?

A. Statement: ∠IKL≅∠JLK

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

B. Statement: ∠IKL and ∠IKC are supplementary.

Reason: Linear Pair Theorem

C. Statement: ∠GJI≅∠JLK

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

D. Statement: ∠GJI and ∠IJL are supplementary.

Reason: Linear Pair Theorem

1. ∠EIJ≅∠GJI given

2. ∠EIJ≅∠IKL For parallel lines cut by a transversal, corresponding angles are congruent.

3. ∠IKL≅∠GJI Transitive Property of Equality

4.

5. ∠IKL and ∠IJL are supplementary. Transitive Property of Equality

+3

Answers (2)

Know the Answer?

Mollie · Answer 1

The correct answer to this is the option:

C. Statement: ∠GJI≅∠JLK

Reason: For parallel lines cut by a transversal, corresponding angles are congruent.

Since the two angles are corresponding angles and the two parallel lines are cut by a transversal.

Abbey Lester · Answer 2

The correct answer is:

D) Statement: ∠GJI and ∠IJL are supplementary; Reason: Linear Pair Theorem

Explanation:

Step 3 states " ∠IKL≅∠GJI Transitive Property of Equality".

Step 5 states " ∠IKL and ∠IJL are supplementary. Transitive Property of Equality".

The inferred piece of information here is that ∠GJI and ∠IJL are supplementary. Since we do not have anything relating ∠IKL and ∠IJL, we must have something relating the two; relating ∠GJI and ∠IJL will work, since we know that ∠IKL≅∠GJI.