Question

name:________ class:______ date:________ activity 2. read and annotate. determine the correct solution for each question. 1) the diagram below illustrates the construction of $overleftrightarrow{ps}$ parallel to $overleftrightarrow{rq}$ through point $p$. which statement justifies this construction? 1) $mangle1 = mangle2$ 2) $mangle1 = mangle3$ 3) $overline{pr}congoverline{rq}$ 4) $overline{ps}congoverline{rq}$ 2) the diagram below shows the construction of line $m$, parallel to line $ell$, through point $p$. which theorem was used to justify this construction? 1) if two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. 2) if two lines are cut by a transversal and the interior angles on the same side are supplementary, the lines are parallel. 3) if two lines are perpendicular to the same line, they are parallel. 4) if two lines are cut by a transversal and the corresponding angles are congruent, they are parallel. 3) explain how you know your solution is correct.

Explanation:

Step1: Analyze question 1

In the construction of parallel lines, corresponding - angle congruence is used. $\angle1$ and $\angle2$ are corresponding angles. If $m\angle1 = m\angle2$, the lines are parallel.

Step2: Analyze question 2

The construction of a line parallel to another through a point uses the fact that if corresponding angles formed by a transversal are congruent, the lines are parallel.

Step3: Justify the solutions

The construction of parallel lines relies on angle - based parallel line criteria. In both cases, the equality of certain angles formed by a transversal and the lines being constructed parallel is key.

Answer:

1. 1) $m\angle1 = m\angle2$
2. 4) If two lines are cut by a transversal and the corresponding angles are congruent, they are parallel.
3. The construction of parallel lines is based on well - known geometric postulates and theorems about parallel lines and transversals. In the first case, the equality of corresponding angles ($\angle1$ and $\angle2$) justifies the construction of parallel lines. In the second case, the overall construction follows the rule that when corresponding angles are made congruent by a transversal across the original line and the constructed line, the two lines are parallel.