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:

1. A right triangle has one \(90^\circ\) angle. Since \(\triangle DEF\) has a \(90^\circ\) angle at \(E\), it is a right triangle. So "Triangle DEF is a right triangle" is true.
2. The sum of angles in a triangle is \(180^\circ\). In a right triangle, the other two angles must be acute (less than \(90^\circ\)) because \(180 - 90=90\), so each of the remaining angles is less than \(90^\circ\). Thus, the angle at vertex \(D\) is acute. "The angle at vertex \(D\) is obtuse" is false (obtuse is greater than \(90^\circ\)), "Triangle DEF is an obtuse triangle" is false (obtuse triangles have one angle greater than \(90^\circ\), not equal), and "The angle at vertex \(F\) is obtuse" is false.

Answer:

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