Question

guided practice
given: (angle 1 cong angle 2)
prove: (ell | m)
what is the missing statement in the proof?
a. (angle 1 cong angle 3)
b. (ell | m)
c. (angle 3 cong angle 2)
d. (angle 1 cong angle 2)

Explanation:

Step1: Recall the property of vertical angles

Vertical angles are congruent. So, if vertical \( \angle3\) and another angle are congruent, and we know \( \angle1\cong\angle2\), we need to find the relation between \( \angle1\) and \( \angle3\).
Since vertical angles are congruent, \( \angle1\cong\angle3\) (because \( \angle3\) and \( \angle1\) are vertical angles in the diagram - when two lines intersect, vertical angles are equal). Then using the transitive property (if \(a = b\) and \(b = c\), then \(a = c\), here \(a=\angle1\), \(b = \angle3\), \(c=\angle2\) after substitution from given \( \angle1\cong\angle2\) and using vertical - angle congruence \( \angle1\cong\angle3\)).

Answer:

A. \( \angle1\cong\angle3\)