Question

list the sides of each triangle in order from shortest to longest.
δmkl with ∠m = 65°, ∠k = 56°, and ∠l = 59°
choose the correct order of the sides from shortest to longest.
a. (overline{lk}), (overline{lm}), (overline{mk})
b. (overline{lm}), (overline{mk}), (overline{lk})
c. (overline{lk}), (overline{mk}), (overline{lm})
d. (overline{lm}), (overline{lk}), (overline{mk})
e. (overline{mk}), (overline{lk}), (overline{lm})
f. (overline{mk}), (overline{lm}), (overline{lk})

Explanation:

Step1: Compare the angles

In $\triangle MKL$, $\angle K = 56^{\circ}$, $\angle L = 59^{\circ}$, $\angle M=65^{\circ}$. So, $\angle K<\angle L<\angle M$.

Step2: Use the angle - side relationship

In a triangle, the side opposite the smaller angle is shorter.

• Side opposite $\angle K$ is $\overline{LM}$.
• Side opposite $\angle L$ is $\overline{MK}$.
• Side opposite $\angle M$ is $\overline{LK}$.

Since $\angle K<\angle L<\angle M$, the sides from shortest to longest are $\overline{LK}$ (opposite $\angle M$), $\overline{LM}$ (opposite $\angle K$), $\overline{MK}$ (opposite $\angle L$).

Answer:

A. $\overline{LK}$, $\overline{LM}$, $\overline{MK}$