Question

if triangle def has a 90° angle at vertex e, which statements are true? select two options.
□ triangle def is an obtuse triangle.
□ the angle at vertex d is acute.
□ the angle at vertex f is obtuse.
□ triangle def is a right triangle.
□ the angle at vertex d is obtuse.

Explanation:

Step1: Recall triangle - type definitions

A right - triangle has one angle equal to 90°. An obtuse - triangle has one angle greater than 90°. An acute angle is an angle less than 90°.

Step2: Analyze triangle DEF

Since ∠E = 90°, triangle DEF is a right - triangle.

Step3: Analyze other angles

In a triangle, the sum of interior angles is 180°. So, ∠D+∠F = 180° - ∠E=180° - 90° = 90°. Thus, both ∠D and ∠F must be acute angles.

Answer:

B. The angle at vertex D is acute.
D. Triangle DEF is a right triangle.