Question

Given three parallel lines EF || GH || IJ intersected by two transversals AB and CD, prove that OM/MK = PN/NL.

A. Corresponding Angles Theorem

B. Alternate Interior Angles Theorem

C. Transitive Property

D. Parallel Lines Converse Theorem

Answer 1

To prove OM/MK = PN/NL, we can use the Parallel Lines Converse Theorem and the Alternate Interior Angles Theorem. By applying the Corresponding Angles Theorem and the Transitive Property, we can establish the required equality.

To prove that OM/MK = PN/NL, we can use the Parallel Lines Converse Theorem.

Since EF || GH and AB and CD are transversals, we can use the Alternate Interior Angles Theorem to conclude that angle AOM is congruent to angle PNL and angle MKO is congruent to angle NLN.

Therefore, by the Corresponding Angles Theorem and the Transitive Property, we have OM/MK = PN/NL.