Question

1. which geometric principle is used to justify the construction below. (1) a line perpendicular to one of two parallel lines is perpendicular to the other. (2) two lines are perpendicular if they intersect to form congruent adjacent angles. (3) when two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel. (4) when two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel. 22. in the accompanying diagram, the bisector of an angle has been constructed. in proving this construction, which reason is used for the congruence involved? (1) sss (2) sas (3) aas (4) asa

Explanation:

Step1: Analyze question 21

In the construction of line \(m\) parallel to line \(\ell\) through point \(P\), we use the property of corresponding - angles. When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.

Step2: Analyze question 22

In the construction of an angle - bisector, we create two triangles. We use the fact that the radii of the arcs are equal, so the three sides of the two triangles formed are equal. By the SSS (Side - Side - Side) congruence criterion, the two triangles are congruent.

Answer:

1. (4) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.
2. (1) SSS