Question

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

Explanation:

• A right - triangle is defined as a triangle with one \(90^{\circ}\) angle. Since triangle \(DEF\) has a \(90^{\circ}\) angle at \(E\), it is a right - triangle.
• The sum of the interior angles of a triangle is \(180^{\circ}\). If one angle (\(\angle E = 90^{\circ}\)), then the sum of the other two angles (\(\angle D+\angle F=180 - 90=90^{\circ}\)). An acute angle is an angle between \(0^{\circ}\) and \(90^{\circ}\), and an obtuse angle is an angle between \(90^{\circ}\) and \(180^{\circ}\). So, \(\angle D\) and \(\angle F\) must be acute.

Answer:

• Triangle \(DEF\) is a right - triangle.
• The angle at vertex \(D\) is acute.