Question

7.
complete the congruence statement:
a.
b.
c.
d.
8.
in the figure, . which of the following statements is false?

and are vertical angles
and are vertical angles

Explanation:

7.

Step1: Recall congruent angles in the figure

In the given figure, by the property of congruent triangles (assuming the triangles are congruent as per the angle - marking pattern), \(\angle DEF\) and \(\angle DFG\) are in corresponding positions.

8.

Step1: Use linear - pair property

Since \(\angle AED\) and \(\angle AEB\) form a linear pair (\(\angle AED+\angle AEB = 180^{\circ}\)), and \(\angle AED = 110^{\circ}\), then \(\angle AEB=180 - 110=70^{\circ}\).

Step2: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. \(\angle AEB\) and \(\angle DEC\) are vertical angles, \(\angle BEC\) and \(\angle AED\) are vertical angles. If \(\angle AED = 110^{\circ}\), then \(\angle BEC=\angle AED = 110^{\circ}\) (vertical angles are equal). \(\angle AEB\) and \(\angle BEC\) are adjacent angles (they share a common side \(BE\)) and not vertical angles.

Answer:

1. A. \(\angle DFG\)
2. \(\angle AEB\) and \(\angle BEC\) are vertical angles