Question

Given: l || m; ∠1 ∠3 Prove: p || q 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

Lines l and m are parallel and p and q are intersecting these parallel lines. It can be concluded that the lines p and q are parallel.

Given information:

Line l is parallel to line m.

Angle 1 is equal to angle 3.

Now, from the figure, angle 1 and angle 3 are corresponding angles that are given to be equal.

The line p makes angle 1 with line l which is equal to angle 3 made by line q and m. Also, lines l and m are parallel. So, the lines p and q should also be parallel because they are making same angle with two parallel lines.

Therefore, it can be concluded that the lines p and q are parallel.

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