https://file.aiquickdraw.com/mathbot/file/172597896424888opvzh3.jpg

In the triangle \( \triangle FGH \), the angles provided are:

- \( \angle F = 60^\circ \)
- \( \angle G = 68^\circ \)
- \( \angle H = 52^\circ \)

To find which side is the shortest, we apply the rule that in any triangle, the shortest side is opposite the smallest angle.

Here are the corresponding sides:
- \( \overline{GH} \) is opposite \( \angle F = 60^\circ \)
- \( \overline{FH} \) is opposite \( \angle G = 68^\circ \)
- \( \overline{FG} \) is opposite \( \angle H = 52^\circ \)

Since \( \angle H = 52^\circ \) is the smallest angle, the shortest side is opposite this angle, which is side \( \overline{FG} \).

Thus, the correct answer is:
- **C. \( \overline{FG} \)**

Let me know if you'd like more details or have any questions! 

Here are 5 related questions:
1. How do you determine the longest side of a triangle given its angles?
2. What is the relationship between the sides and angles in a triangle?
3. Can this technique of comparing angles and sides be used in right triangles?
4. How do we solve for the sides if all three angles and one side are given?
5. What are the rules for the sum of angles in any triangle?

**Tip:** Always remember that the largest side of a triangle is opposite the largest angle, and the smallest side is opposite the smallest angle.

In ∆FGH, m∠F = 60°, m∠G = 68°, and m∠H = 52°. Which side of ∆FGH is the shortest?

This problem explores the relationship between angles and sides in a triangle. Given angles F = 60°, G = 68°, and H = 52°, students can determine the shortest side by identifying the side opposite the smallest angle. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation