Question

In the figure AB||CD and EIA is congruent to GJB

Answer 1

The answers 
1)  D. (TRANSITIVE PROPERTY OF CONGRUENCY)
2)  C. (LINEAR PAIR THEOREM)
3)  D. TRANSITIVE PROPERTY OF CONGRUENCY) to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.
4)  C. (CONGRUENT SUPPLEMENTS THEOREM)

Answer 2

Answer:

Corresponding pairs

Linear Pair

Substitution Property

Step-by-step explanation:

Given line AB║CD,

⇒ ∠EIJ & ∠IKL are corresponding pairs and hence equal.

llly, with the same reason ∠GJI and ∠JLK are also the corresponding pairs and hence also equal.

Given ∠EIJ ≅ ∠GJI,

therefore due to above reason of corresponding angles ∠IKL ≅ ∠JLK

Now, ∠JLK and ∠JLD are linear pair

∴ these are supplementary  ∠JLK + ∠JLD=180° → (1)

Given, m∠IKL = m∠JLK → (2)

From substitution property,

               ∠IKL + ∠JLD = 180°

Therefore,   ∠IKL and ∠JLD are supplementary.