Question

1. choose the correct answer.

order the angles of δdef from smallest to largest.
de = 3 cm; ef = 5 cm; df = 6 cm
de < ef < df, so _____
image of triangle def with de = 3 cm, ef = 5 cm, df = 6 cm
options:
∠e < ∠d < ∠f
∠d < ∠f < ∠e
∠f < ∠d < ∠e

Explanation:

Step1: Recall Triangle Angle-Side Relationship

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

• Side \( DE = 3 \, \text{cm} \) is opposite \( \angle F \).
• Side \( EF = 5 \, \text{cm} \) is opposite \( \angle D \).
• Side \( DF = 6 \, \text{cm} \) is opposite \( \angle E \).

Step2: Order Sides and Corresponding Angles

Given \( DE < EF < DF \) (i.e., \( 3 < 5 < 6 \)), their opposite angles will follow the same order. So the angles opposite are \( \angle F < \angle D < \angle E \) (since \( DE \) opposite \( \angle F \), \( EF \) opposite \( \angle D \), \( DF \) opposite \( \angle E \)).

Answer:

\(\angle F < \angle D < \angle E\) (the third option: \(\boldsymbol{\angle F < \angle D < \angle E}\))