Question

Given: l || m; ∠1 ∠3 Prove: p || q Horizontal and parallel lines l and m are intersected by parallel lines p and q. At the intersection of lines l and p, the uppercase left angle is angle 1. At the intersection of lines q and l, the bottom right angle is angle 2. At the intersection of lines q and m, the uppercase left angle is angle 3.

Complete the missing parts of the paragraph proof.
We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because __________________ . We see that _______ is congruent to ______ by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the ______________ .

Answer 1

Answer:

It is given

2 is congruent to 3

converse alternate exteriour angles theroum

Step-by-step explanation:

Answer 2

The missing part of the proof is
mentioned in the question, 2 is congruent to 3,
converse alternate angles theorem.

What are parallel lines?

parallel lines are those lines, the perpendicular distance between them remains same and both lines meet at infinite.

Since
∡1 = 3∡
∡2 = 3∡
we can conclude that

We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because mentioned in the question  . We see that 2 is congruent to 3 by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the converse alternate angles theorem.

Thus, the required data has been filled which is mentioned in the question, 2 is congruent to 3, converse alternate angles theorem.

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