Question

prepare
use the numbered angles in the diagram to answer each question.

1. which angles form vertical angles?
2. which angles are congruent?

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are pairs of opposite angles formed by two intersecting lines.

Step2: Identify vertical - angle pairs

For the given diagram:

• When two lines intersect, \(\angle1\) and \(\angle3\) are opposite each other, so \(\angle1\) and \(\angle3\) are vertical angles.
• \(\angle4\) and \(\angle6\) are opposite each other, so \(\angle4\) and \(\angle6\) are vertical angles.
• \(\angle2\) and \(\angle5\) are opposite each other, so \(\angle2\) and \(\angle5\) are vertical angles.

Step3: Recall the property of congruent angles

Vertical angles are congruent. Also, if there are parallel lines and transversals (assuming the lines \(l_1\), \(l_2\), \(l_3\) follow the rules of parallel - line angle relationships), but based on the vertical - angle property alone:
Since vertical angles are congruent, \(\angle1\cong\angle3\), \(\angle4\cong\angle6\), \(\angle2\cong\angle5\)

Answer:

1. The vertical - angle pairs are \(\angle1\) and \(\angle3\), \(\angle4\) and \(\angle6\), \(\angle2\) and \(\angle5\).
2. The congruent - angle pairs are \(\angle1\cong\angle3\), \(\angle4\cong\angle6\), \(\angle2\cong\angle5\)