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.

Explanation:

Step1: Given information

They are given in the problem statement.

Step2: Identify alternate - interior angles

$\angle2$ is congruent to $\angle3$ by the alternate - interior angles theorem since $l\parallel m$.

Step3: Use transitive property

Since $\angle1\cong\angle3$ and $\angle2\cong\angle3$, then $\angle1\cong\angle2$ by the transitive property.

Step4: Prove parallel lines

Lines $p$ and $q$ are parallel by the corresponding - angles postulate (if corresponding angles are congruent, then the lines are parallel, and $\angle1$ and $\angle2$ are corresponding angles).

Answer:

We know that angle 1 is congruent to angle 3 and that line $l$ is parallel to line $m$ because it is given. We see that $\angle2$ is congruent to $\angle3$ 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 corresponding - angles postulate.