Question

I'm giving 100 points to someone who would please help me! Thank you so much! Pleaseeeee!!!

Answer 1

See below

Explanation:

We are given:

• JM ║ KN
• ∠1 ≅ ∠2
• ∠3 ≅ ∠4

and we are asked to prove
KM ║ LN

Proof
Given JM ║ KN, by the corresponding angles postulate if two parallel lines are cut by a transversal then the corresponding angles are congruent

Therefore
∠1 ≅ ∠3
and
∠2 ≅ ∠4

Since ∠1 ≅ ∠2 and ∠3 ≅ ∠4 we can conclude that ∠2 ≅ ∠4

By the converse of the Corresponding Angles Postulate, if two lines are cut by a transversal and corresponding angles are congruent the two lines are parallel

Since ∠2 and ∠4 are formed by the transversal JKL intersecting lines KM and LN and since they are congruent we can conclude

KM ║ LN

Hope that helps