Question

1. choose the correct answer.

order the sides of δxyz from shortest to longest.
∠x = 35°; ∠y = 65°; ∠z = 80°
∠x < ∠y < ∠z, so:
image of triangle xyz with angles at x: 35°, y: 65°, z: 80°
options:

• xz < yz < xy
• yz < yz < xy (likely a typo)
• yz < xz < xy

Explanation:

Step1: Recall Triangle Side-Angle Relationship

In a triangle, the larger the angle, the longer the side opposite to it. So we first identify the sides opposite each angle.

• Opposite \( \angle X = 35^\circ \): Side \( YZ \)
• Opposite \( \angle Y = 65^\circ \): Side \( XZ \)
• Opposite \( \angle Z = 80^\circ \): Side \( XY \)

Step2: Order Angles and Corresponding Sides

Given \( \angle X < \angle Y < \angle Z \) (i.e., \( 35^\circ < 65^\circ < 80^\circ \)), the sides opposite these angles will follow the same order. So the order of sides from shortest to longest is:
Side opposite smallest angle (\( \angle X \)) < Side opposite middle angle (\( \angle Y \)) < Side opposite largest angle (\( \angle Z \))
Which is \( YZ < XZ < XY \)

Answer:

\( YZ < XZ < XY \) (corresponding to the third option: \( YZ < XZ < XY \))