Question

If triangle DEF has a 90° angle at vertex E, which statements are true? Check all that apply.

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

Answer 1

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

Answer 2

The answer is

The angle at vertex D is acute

Triangle DEF is a right triangle

Explanation:

Statements

case A) Triangle DEF is an obtuse triangle

The statement is false

The triangle DEF has no angle greater than
`90\°`

Triangle DEF is a right triangle, because has an angle equal to
`90\°`

case B) The angle at vertex D is acute

The statement is true

Because

∠D+∠F=
`90\°`

so

Angle D is less than
`90\°`

case C) The angle at vertex F is obtuse

The statement is false

Because

∠D+∠F=
`90\°`

so

Angle F is not greater than
`90\°`

case D) Triangle DEF is a right triangle

The statement is true

Because, angle at vertex E is equal to
`90\°`

case E) The angle at vertex D is obtuse

The statement is false

Because

∠D+∠F=
`90\°`

so

Angle D is not greater than
`90\°`