Question

use the figure to answer the question. *not drawn to scale select all of the statements that are sufficient to determine that △jlm is isosceles? a. jk = kl b. jm = ml c. jl = mk d. m∠mjk = m∠mlk e. m∠mjl = m∠jml f. m∠jmk = m∠lmk

Explanation:

Step1: Recall isosceles - triangle definition

An isosceles triangle has two equal - length sides or two equal - measure angles.

Step2: Analyze side - length conditions

If \(JM = ML\), then by the definition of an isosceles triangle (a triangle with two equal sides), \(\triangle JLM\) is isosceles. So statement B is sufficient.

Step3: Analyze angle - measure conditions

If \(\angle MJK=\angle MLK\), then the triangle has two equal - measure base angles. In a triangle, if two angles are equal, the sides opposite those angles are equal, and the triangle is isosceles. So statement D is sufficient.

Answer:

B. \(JM = ML\), D. \(m\angle MJK=m\angle MLK\)