Question

naming angles, sides of angles, and vertices

(a) name the sides of ( angle gfe ).
( overrightarrow{fg} ) and ( overrightarrow{fg} )

(b) write two other names for ( angle 2 ).
( angle efh ) and ( angle hfe )

(c) name the vertex of ( angle 1 ).

Explanation:

Step1: Recall the definition of an angle's sides

An angle is formed by two rays with a common endpoint. For \( \angle GFE \), the two rays (sides) are \( \overrightarrow{FG} \) and \( \overrightarrow{FE} \).

Step2: Recall the naming rules for angles

An angle can be named in three ways: by its vertex (if there is only one angle at that vertex), by a number inside the angle, or by three points (with the vertex in the middle). For \( \angle 2 \), since the vertex is \( F \), and the rays are \( \overrightarrow{FE} \) and \( \overrightarrow{FH} \), two other names are \( \angle EFH \) and \( \angle HFE \).

Step3: Recall the definition of an angle's vertex

The vertex of an angle is the common endpoint of the two rays forming the angle. For \( \angle 1 \), the two rays are \( \overrightarrow{FG} \) and \( \overrightarrow{FE} \), so the vertex is \( F \).

Answer:

(a) \( \overrightarrow{FG} \) and \( \overrightarrow{FE} \)
(b) \( \angle EFH \) and \( \angle HFE \)
(c) \( F \)