Question

name the longest and shortest side in each triangle. 27) a) $overline{lm},overline{mn}$ b) $overline{mn},overline{ln}$ c) $overline{ln},overline{mn}$ d) $overline{mn},overline{lm}$ 28) a) $overline{bc},overline{ab}$ b) $overline{ac};overline{bc}$ and $overline{ab}$ c) $overline{ab},overline{ac}$ d) $overline{bc};overline{ac}$ and $overline{ab}$ 29) a) $overline{jl},overline{jk}$ b) $overline{jl},overline{kl}$ c) $overline{jl};overline{kl}$ and $overline{jk}$ d) $overline{jk},overline{jl}$ 30) a) $overline{kj},overline{lk}$ b) $overline{lk},overline{lj}$ c) $overline{lk},overline{kj}$ d) $overline{kj},overline{lj}$

Explanation:

Step1: Recall angle - side relationship

In a triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle.

Step2: Analyze triangle in 27

In $\triangle LMN$, $\angle L = 99^{\circ}$, $\angle M=42^{\circ}$, $\angle N = 39^{\circ}$. The largest angle is $\angle L$ and the side opposite it is $MN$. The smallest angle is $\angle N$ and the side opposite it is $LM$. So the longest side is $MN$ and the shortest side is $LM$.

Step3: Analyze triangle in 28

In $\triangle ABC$, $\angle A = 80^{\circ}$, $\angle B = 50^{\circ}$, $\angle C=50^{\circ}$. The largest angle is $\angle A$ and the side opposite it is $BC$. The smallest angles are $\angle B$ and $\angle C$, and the sides opposite them are $AC$ and $AB$. So the longest side is $BC$ and the shortest sides are $AC$ and $AB$.

Step4: Analyze triangle in 29

In $\triangle JKL$, $\angle K = 110^{\circ}$, $\angle J = 30^{\circ}$, $\angle L = 40^{\circ}$. The largest angle is $\angle K$ and the side opposite it is $JL$. The smallest angle is $\angle J$ and the side opposite it is $KL$. So the longest side is $JL$ and the shortest side is $KL$.

Step5: Analyze triangle in 30

In $\triangle JKL$, $\angle L = 65^{\circ}$, $\angle J = 55^{\circ}$, $\angle K = 60^{\circ}$. The largest angle is $\angle L$ and the side opposite it is $JK$. The smallest angle is $\angle J$ and the side opposite it is $LK$. So the longest side is $JK$ and the shortest side is $LK$.

Answer:

1. D. $MN, LM$
2. B. $BC; AC$ and $AB$
3. B. $JL, KL$
4. A. $KJ, LK$