Question

Match the reasons with the statements in the proof.

Given:
j | | k
m 1 = m 3

Prove:
l | | m

Answer 1

Answer: please see image attached. Let me know if you have questions.

Answer 2

By the corresponding angle theorem : The corresponding angles made by a same transversal on two parallel lines are equal in measure.

By the converse of alternate angles : When alternative angles in two lines by same transversal are equal then these lines are parallel to each other,

Now, given,

j ║ k

m∠1 = m∠3

Prove: l ║ m,

Thus, the column proof would be,

Statement Reason

1. j ║k, m∠1 = m∠3 Given

2. m∠1 = m∠2 If lines are ║, then corresponding angles are =

3. m∠2 = m∠3 Substitution

4. l ║ m If alternative angles are =, then lines are ║