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What is the missing step in the proof?

AStatement: ∠IKL≅∠JLK

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

BStatement: ∠IKL and ∠IKC are supplementary.

Reason: Linear Pair Theorem

CStatement: ∠GJI≅∠JLK

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

DStatement: ∠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

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

Verified Answer :

Hagrid

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.

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.

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