Question

triangle knm is shown. what is true about the sides of knm?

kn = nm
kn + nm = km
km = 2(nm)
kn = \frac{1}{2}km

Explanation:

In triangle \( KNM \), the angles at \( K \) and \( M \) are both \( 25^\circ \). By the Isosceles Triangle Theorem, sides opposite equal angles are equal. The sides opposite \( \angle M \) (which is \( 25^\circ \)) is \( KN \), and the side opposite \( \angle K \) (which is \( 25^\circ \)) is \( NM \). So \( KN = NM \).

For the other options:

• The triangle inequality theorem states that the sum of two sides of a triangle must be greater than the third side, so \( KN + NM > KM \), not equal.
• There's no information to suggest \( KM = 2(NM) \) or \( KN=\frac{1}{2}KM \) as the triangle isn't a special right triangle or has any markings indicating such a relationship.

Answer:

A. \( KN = NM \)