Question

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

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.

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.