Help Please!
In the figure, AB║CD and ∠EIA is congruent to ∠GJB Complete the following statements to prove that ∠IKL is congruent to ∠DLH.
∠EIA is congruent to ∠IKC and ∠GJB is congruent to ∠ JLD because they are corresponding angles of parallel lines cut by a transversal.
So, if , ∠EIA is congruent to ∠GJB then ∠IKC is congruent to ∠ JLD by the
A. (SUBTRACTION PROPERTY OF EQUALITY)
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 ANGLE THEOREM)
B. (CONGRUENT SUPPLEMENTS THEOREM)
C. (LINEAR PAIR THEOREM)
m∠IKL + m∠IKC = 180° (1)
∠IKC congruent to ∠ JLD, so m∠IKC = m∠JLD (2)
Applying the
(A. SUBTRACTION PROPERTY OF EQUALITY)
(B. SUBTRACTION 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 congruent to ∠DLH by the
A. (VERTICAL ANGLES THEOREM)
B. (DEFINITION OF SUPPLEMENTARY ANGLES)
C. (CONGRUENT SUPPLEMENTS THEOREM)
D. (LINEAR PAIR THEOREM)
