Question

in the diagram below, (overleftrightarrow{xy}) is the perpendicular bisector of (overline{jk}). which of the following statements must be true? check all that apply. a. (overleftrightarrow{xy}) and (overline{jk}) form four right angles b. (xp = yp) c. (jp = kp) d. (mangle jpx=90^{circ})

Explanation:

Step1: Recall perpendicular - bisector properties

A perpendicular bisector of a line segment is perpendicular to the segment and bisects it.

Step2: Analyze option A

Since $\overline{XY}$ is the perpendicular bisector of $\overline{JK}$, $\overline{XY}$ and $\overline{JK}$ intersect at a right - angle. At the intersection point $P$, four right - angles are formed. So, $\overline{XY}$ and $\overline{JK}$ form four right angles.

Step3: Analyze option B

There is no information given to suggest that $XP = YP$. The perpendicular bisector property is about the line segment $\overline{JK}$, not about the lengths $XP$ and $YP$.

Step4: Analyze option C

By the definition of a bisector, if $\overline{XY}$ is the bisector of $\overline{JK}$, then it divides $\overline{JK}$ into two equal parts. So, $JP=KP$.

Step5: Analyze option D

Since $\overline{XY}$ is perpendicular to $\overline{JK}$, the angle $\angle JPX = 90^{\circ}$.

Answer:

A. $\overline{XY}$ and $\overline{JK}$ form four right angles
C. $JP = KP$
D. $m\angle JPX=90^{\circ}$