Question

triangle knm is shown.
what is true about the sides of knm?
options: km = 2(nm); kn + nm = km; kn = nm; kn = 1/2 km

Explanation:

Step1: Analyze triangle angles

In $\triangle KNM$, $\angle K = 25^\circ$, $\angle M = 25^\circ$, $\angle N = 130^\circ$. Angles $\angle K$ and $\angle M$ are equal.

Step2: Apply isosceles triangle theorem

In a triangle, equal angles correspond to equal opposite sides. So, side opposite $\angle K$ (which is $NM$) and side opposite $\angle M$ (which is $KN$) are equal. Thus, $KN = NM$.

Step3: Evaluate other options

• For $KM = 2(NM)$: No basis from angle - side relations here.
• For $KN + NM = KM$: Triangle inequality states $KN + NM>KM$, so this is false.
• For $KN=\frac{1}{2}KM$: No basis from angle - side relations here.

Answer:

KN = NM