Question

Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles.

Answer 1

Answer:

PROOF IN STEP BY STEP SOLUTION

Step-by-step explanation:

Given : ∠EIJ ≅ ∠IKL and ∠GJI ≅ ∠JLK  they are corresponding angles for parallel lines cut by a transversal.

To Prove : i) if ∠EIJ ≅ ∠GJI, then ∠IKL ≅ ∠JLK

                  ii)∠JLK and ∠JLD are supplementary angles i.e.

                       m∠JLK + m∠JLD = 180°.

                  iii) if ∠IKL ≅ ∠JLK, m∠IKL = m∠JLK.

                     Thus m∠IKL + m∠JLD = 180°

Proof: i) we are given that ∠EIJ ≅ ∠IKL and ∠GJI ≅ ∠JLK

             if ∠EIJ ≅ ∠GJI

             ∠GJI ≅∠IKL ( alternate interior angles) (equation 1)

              ∠GJI ≅ ∠JLK (given) (equation 2)

by  equation 1 and equation 2

              ⇒∠IKL ≅ ∠JLK

ii) ∠JLK and ∠JLD are linear pairs and sum of linear pairs are 180°

so  m∠JLK + m∠JLD = 180° i.e. ∠JLK and ∠JLD are supplementary angles.

iii) ∠IKL ≅ ∠JLK ( by i part )

   ∠IKL = ∠JLK  (a)

 ∠JLK + ∠JLD = 180° ( by ii part ) ---(b)

so we can write ∠IKL at place of ∠JLK in (b) by (a)

⇒∠IKL + ∠JLD = 180° i.e. supplementary angles .