Question

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 ___________ (substitution property of equality, subtraction property of equality , or symmetry property of equality.) . Angle JLK and ∠JLD are supplementary angles by the _____________________ (vertical angles theorem, congruent supplements theroem, or linear pair theroem.) so m∠JLK + m∠JLD = 180°. By the (substitution property of equality reflexive property of equality, or division property of equality) , m∠IKL + m∠JLD = 180°. Therefore, ∠IKL and ∠JLD are supplementary angles by definition.

Answer 1

Answer:

1st blank: substitution property of equality

2nd blank: linear pair theorem

3rd blank: substitution property of equality

Step-by-step explanation:

1st blank

∠EIJ ≅ ∠GJI (eq. 1)

∠EIJ ≅ ∠IKL (eq. 2)

∠GJI ≅ ∠JLK (eq. 3)

Substituting eq. 3 into eq. 1:

∠EIJ ≅ ∠JLK

and then, substituting eq. 2:

∠IKL ≅ ∠JLK

which means that m∠IKL = m∠JLK

2nd blank

The Linear Pair Theorem states that two angles that form a linear pair are supplementary

3rd blank

m∠JLK + m∠JLD = 180°

Substituting with the previous result:

m∠IKL + m∠JLD = 180°