Question

Use the figure to answer the question.

Information
A figure shows triangle J L M. A line segment goes from angle M to point K on segment J L.

Question
Select ,begin emphasis,all,end emphasis, of the statements that are sufficient to determine that triangle J L M is isosceles?

Answer options with 6 options
A.
J K equals K L

B.
J M equals M L

C.
J L equals M K

D.
the measure of angle M J K equals the measure of angle M L K

E.
the measure of angle M J L equals the measure of angle J M L

F.
the measure of angle J M K equals the measure of angle L M K

Answer 1

B, D, and E.

Brief reasons:
- B: JM = ML directly makes the triangle isosceles.
- D: ∠MJK = ∠MLK are the base angles ∠MJL and ∠MLJ, so the base angles are equal → JM = ML.
- E: ∠MJL = ∠JML means two angles of the triangle are equal → the two opposite sides are equal (ML = JL), so the triangle is isosceles.

(A, C, and F are not sufficient.)