Question

use the given information to answer each question. explain your reasoning
how do the measures of ( widehat{kl} ) and ( widehat{lm} ) compare?

__ ( mathrm{kl} ) is equal to arc ( mathrm{lm} ) because ( mathrm{lj} ) is a and intersects the ( mathrm{mk} ) at a angle. it also __ the arcs

word bank:
right chord obtuse congruent similar bisects parallel arc acute diameter radius

Explanation:

Step1: Recall the theorem

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arcs.

Step2: Analyze the given circle

In the circle, \( LJ \) is a diameter (passes through the center \( O \)). \( MK \) is a chord. \( LJ\perp MK \) (right - angle at \( N \)).

Step3: Apply the theorem

By the theorem, the diameter \( LJ \) bisects the chord \( MK \) and its arcs \( \overarc{KL} \) and \( \overarc{LM} \). So, \( \overarc{KL}\) and \( \overarc{LM}\) are congruent.

Answer:

Congruent, diameter, chord, right, bisects