Question

1. order the angles of △ghi from smallest to largest.

(image of triangle ghi with sides: gh = 4 cm, hi = 6 cm, gi = 8 cm. below the image, there are three dropdowns and options: a. ∠h, b. ∠i, c. ∠g)

Explanation:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the larger the side length, the larger the opposite angle. So we first identify the side lengths and their opposite angles.

• Side opposite \( \angle G \): \( HI = 6 \) cm
• Side opposite \( \angle I \): \( GH = 4 \) cm
• Side opposite \( \angle H \): \( GI = 8 \) cm

Step2: Order the Sides by Length

Order the sides from shortest to longest: \( GH = 4 \) cm (shortest), \( HI = 6 \) cm, \( GI = 8 \) cm (longest).

Step3: Order the Angles by Opposite Sides

Since the angle opposite the shortest side is the smallest, and vice versa:

• Opposite \( GH \) (4 cm) is \( \angle I \), so \( \angle I \) is smallest.
• Opposite \( HI \) (6 cm) is \( \angle G \), so \( \angle G \) is next.
• Opposite \( GI \) (8 cm) is \( \angle H \), so \( \angle H \) is largest.

Answer:

b. \( \angle I \), c. \( \angle G \), a. \( \angle H \)