Answer:
Statements B and D are true.
Step-by-step explanation:
We are asked to choose the correct statements about triangle DEF if it has a 90° angle at vertex E.
Let us see our given choices one by one.
A. Triangle DEF is an obtuse triangle.
Since angle D is a 90 degree angle, so other two angles will add up-to 90 degrees according to angle sum property. We know that an obtuse angle's measure is more than 90 degrees. Since none of the given angles is greater than 90 degrees, therefore, statement A is false.
B. The angle at vertex D is acute.
We know that measure of an acute angle is less than 90 degrees.
We have been given that angle E of the triangle DEF is 90 degrees, so sum of other two angles (D and F) will be 90 degrees.
Since both angles D and F add up-to 90 degrees, therefore, both D and F are acute angles and statement B is true.
C. The angle at vertex F is obtuse.
We have already proved that angles D and F are acute angles. Therefore, statement C is false.
D. Triangle DEF is a right triangle.
We know that a right triangle is a triangle whose one angle is a right angle (90 degrees).
Since triangle DEF has a 90° angle at vertex E, therefore triangle DEF is a right triangle and statement D is true.
E. The angle at vertex D is obtuse.
We already proved that angle at vertex D is an acute angle, therefore, statement E is false.
