Question

1. determine whether the diagram gives enough information to conclude that the statement is true:

∠6 = ∠7
a. yes
b. no

1. determine whether the diagram gives enough information to conclude that the statement is true:

∠1 = ∠3
a. yes
b. no

Explanation:

1. For \(\angle6=\angle7\)

• Step1: Analyze the relationship between \(\angle6\) and \(\angle7\)

There is no information in the diagram (such as parallel lines, equal - side triangles etc.) that would imply \(\angle6=\angle7\). Just because they are adjacent angles formed by intersecting lines does not mean they are equal.

2. For \(\angle1=\angle3\)

• Step1: Recall the property of vertical angles

When two lines intersect, vertical angles are equal. Lines \(c\) and \(d\) intersect, and \(\angle1\) and \(\angle3\) are vertical angles.

Answer:

1. B. No
2. A. Yes