Question

use the diagram to name the included angle between the given pair of sides.1 \\( \overline { g h } \\) and \\( \overline { h i } \\)2 \\( \overline { h i } \\) and \\( \overline { i g } \\)3 \\( \overline { i g } \\) and \\( \overline { h g } \\)

Explanation:

Step1: Recall the definition of included angle

The included angle between two sides of a triangle is the angle formed by those two sides.

Step2: Analyze each pair

• For pair \( \overline{GH} \) and \( \overline{HI} \): The angle formed by \( \overline{GH} \) and \( \overline{HI} \) is \( \angle HIG \).
• For pair \( \overline{HI} \) and \( \overline{IG} \): The angle formed by \( \overline{HI} \) and \( \overline{IG} \) is \( \angle HIG \).
• For pair \( \overline{IG} \) and \( \overline{HG} \): The angle formed by \( \overline{IG} \) and \( \overline{HG} \) is \( \angle JGI \).

Answer:

1. \( \angle HIG \)
2. \( \angle HIG \)
3. \( \angle JGI \)