Question

Which of the following are valid names for the triangle below? Check all that apply.



A. EJR
B. KE
C. JE
D. KEJ
E. JAOE
F. JKE"

Answer 1

D. KEJ
F. JKE
These are the valid names of the triangle

Answer 2

In this problem
You have a triangle with 3 sides labeled A, R, O and 3 vertices labeled J, K, E.
To name a triangle, what you do is simply list all of its vertices.
The order doesn't matter.
So
let's take a look at all the possible choices.  
  A. EJR - Nope.E and J are OK. But R is the line segment.
  B. KE - Nope. K and E is OK, but Only has 2 of the vertices.  
  C. JE - Nope. J and E is OK, but Only has 2 of the vertices.   
  D. KEJ - Yes. All three vertices have been named. This is an acceptable name for the triangle. 
  E. JAOE - Nope. Only has 2 of the vertices and A and O are line segments
  F. JKE - Yes. All three vertices have been named. This is an acceptable name for the triangle.

therefore

the answer is
KEJ and JKE