Question

In the figure, AB || CD and ∠EIJ ≅ ∠GJI. Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles. It is given that ∠EIJ ≅ ∠GJI. Also, ∠EIJ ≅ ∠IKL and ∠GJI ≅ ∠JLK, as they are corresponding angles for parallel lines cut by a transversal. By the definition of congruent angles, m∠EIJ = m∠GJI, m∠EIJ = m∠IKL, and m∠GJI = m∠JLK. So, m∠IKL = m∠JLK by the . Angle JLK and ∠JLD are supplementary angles by the , so m∠JLK + m∠JLD = 180°. By the , m∠IKL + m∠JLD = 180°. Therefore, ∠IKL and ∠JLD are supplementary angles by definition.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

The proof is explained below.

Step-by-step explanation:

Given AB || CD, and the two pairs ∠EIJ ≅ ∠IKL and ∠GJI ≅ ∠JLK are the corresponding pair of angles hence equal.

∴ m∠EIJ = m∠IKL and m∠GJI = m∠JLK

By definition of congruent angles, m∠EIJ = m∠GJI

⇒ m∠IKL = m∠JLK   →   (1)

As ∠JLK and ∠JLD are linear pair therefore, supplementary

m∠JLK + m∠JLD = 180°

Using equation (1), put  m∠JLK = m∠IKL

∴ m∠IKL + m∠JLD = 180°

Hence, ∠IKL and ∠JLD are supplementary angles