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

In other words, A, D.

Explanation:

Answer 2

draw a diagram (shown below as attachment)

check each option

1st one: obtuse triangle
osbuse means that the triangle has an angle more than 90 degrees
remember that all angles add to 180
90 is one
90+D+F=180
D+F=90
so those 2 mystery angles both have to be less than 90 so therefor none of them can be obtuse
not 1st option


2nd: angle at D is acute
acute means less than 90
so we remember that
D+F=90
no angle can be 0 so let's say F is a very small number like 0.0001
then D would be 89.9999
still less than 90, it is acute
this 2nd optin is right

3rd: angle at F is obtuse
wrong, from 1st one, no obtuse angles
3rd option is wrong

4th: right triangle
duh, a right triangle has a right angle in it
90 degrees is a right angle
yes
4th optin is right

5th: D is obtuse
naw, fam. no obtuse angles here



the right answers are 2nd and 4th or
The angle at vertex D is acute and
Triangle DEF is a right triangle