Question

what is the missing step in the proof? given: ab || cd, and ∠eij ≅ ∠gji (figure). prove: ∠ikl and ∠ijl are supplementary. statement: ∠ikl ≅ ∠jlk reason: for parallel lines cut by a transversal, corresponding angles are congruent. statement: ∠ikl and ∠ikc are supplementary. reason: linear pair theorem statement: ∠gji ≅ ∠jlk reason: for parallel lines cut by a transversal, corresponding angles are congruent. statement: ∠gji and ∠ijl are supplementary. reason: linear pair theorem

statement	reason
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

Explanation:

Step1: Analyze the goal

We want to prove that $\angle IKL$ and $\angle IJL$ are supplementary. We know $\angle IKL\cong\angle GJI$ from step 3.

Step2: Recall angle - relationships

Since $AB\parallel CD$, we need to find a relationship between $\angle GJI$ and $\angle IJL$.

Step3: Identify the correct step

$\angle GJI$ and $\angle IJL$ are a linear - pair. By the Linear Pair Theorem, linear pairs of angles are supplementary. So the missing step is "Statement: $\angle GJI$ and $\angle IJL$ are supplementary. Reason: Linear Pair Theorem"

Answer:

Statement: $\angle GJI$ and $\angle IJL$ are supplementary. Reason: Linear Pair Theorem