Question

use the figure to complete each part.
(a) name the sides of ∠2.
□ and □
(b) write two other names for ∠1.
□ and □
(c) name the vertex of ∠hfe.
□

Explanation:

(a) Name the sides of ∠2

Step1: Recall the definition of an angle's sides

An angle is formed by two rays with a common endpoint. For ∠2, the two rays (sides) are \( \overrightarrow{FH}\) and \( \overrightarrow{FE}\).

(b) Write two other names for ∠1

Step1: Use vertex - based naming

One way to name an angle is by using the vertex. Since the vertex is \(F\), and the angle is between \( \overrightarrow{FG}\) and \( \overrightarrow{FE}\), we can use \( \angle GFE\). Another way is to use only the vertex (when there is no ambiguity). So \( \angle F\) (assuming no other angles at \(F\) would cause confusion).

(c) Name the vertex of ∠HFE

Step1: Recall the vertex definition

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

Answer:

(a) \( \overrightarrow{FH}\) and \( \overrightarrow{FE}\)
(b) \( \angle GFE\) and \( \angle F\)
(c) \(F\)