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Two parallel lines AB and CD are intersected by a transversal line EF that intersects AB at a point I and CD at a point K. Another transversal line GH is drawn right to GH and intersects AB at a point J and CD at point L.
In the figure, and ∠EIA ≅ ∠GJB. Complete the following statements to prove that ∠IKL ≅ ∠DLH.
∠EIA ≅ ∠IKC and ∠GJB ≅ ∠JLD because they are corresponding angles of parallel lines cut by a transversal.
So, if ∠EIA ≅ ∠GJB, then ∠IKC ≅ ∠JLD by the ________
A. Subtraction of Property
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs of supplementary angles by the ____
A. Vertical Angles Theorem
B. Congruent Supplements Theorem
C. Linear Pair Theorem
.
m∠IKL + m∠IKC = 180° (1)
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD (2)
Applying the _____
A. Subtraction Property of Equality
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency
to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.
Therefore, ∠IKL and ∠JLD are supplementary angles.
We've already shown that ∠DLH and ∠JLD are supplementary angles. Therefore, ∠IKL ≅ ∠DLH by the ____
A. Vertical Angeles Theorem
B. Definition of Supplementary Angles
C. Congruent Supplements Theorem
D. Linear Pair Theorem
.
