Question

which of the following describes km? check all that apply. a. angle bisector b. perpendicular bisector c. median d. altitude (2x + 5)° (3x - 6)°

Explanation:

Step1: Recall angle - bisector definition

An angle - bisector divides an angle into two equal angles. So we set up the equation \(2x + 5=3x - 6\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(2x+5-2x=3x - 6-2x\), which gives \(5=x - 6\). Then add 6 to both sides: \(5 + 6=x-6 + 6\), so \(x = 11\).

Step3: Check the properties of \(KM\)

Since \(2x+5=3x - 6\), the angle \(\angle JKL\) is divided into two equal angles by \(KM\). By the definition of an angle - bisector, \(KM\) is an angle - bisector of \(\angle JKL\). There is no information to suggest it is a median (a line segment joining a vertex to the mid - point of the opposite side), an altitude (a perpendicular line from a vertex to the opposite side), or a perpendicular bisector (a line that is perpendicular to a segment and bisects it).

Answer:

A. angle bisector