Question

select the correct answer from each drop - down menu.
given: m is the midpoint of segment gh.
angles jgm and khm are right angles.
prove: (jg = kh)
complete the proof.
it is given that m is the midpoint of segment gh. therefore, segment gm is congruent to segment hm by the definition of a midpoint. it is also given that angles jgm and khm are right angles. thus, drop - down option because all right angles are congruent. since vertical angles are congruent by the vertical angles theore.... then, it follows that (\triangle jmgcong\triangle kmh) by the drop - down option criteria. in congruent triangles, correspo.... in conclusion (jg = kh) by definition of congruent angles.
drop - down options: angle jmg is congruent to angle kmh; angle mjg is congruent to angle mkh; angle jgm is congruent to angle khm; angle jmg is congruent to angle khm

Explanation:

Step1: Identify midpoint segment congruence

Since $M$ is the midpoint of $\overline{GH}$, $\overline{GM} \cong \overline{HM}$ (definition of midpoint).

Step2: Identify right angle congruence

$\angle JGM$ and $\angle KHM$ are right angles, so $\angle JGM \cong \angle KHM$ (all right angles are congruent).

Step3: Identify vertical angle congruence

Vertical angles $\angle JMG$ and $\angle KMH$ are congruent (vertical angles theorem), which matches the correct dropdown option: angle JMG is congruent to angle KMH.

Step4: Prove triangle congruence

$\triangle JMG \cong \triangle KMH$ by the ASA (Angle-Side-Angle) criteria.

Step5: Corresponding parts congruence

Corresponding sides $\overline{JG} \cong \overline{KH}$, so $JG = KH$ (definition of congruent segments).

Answer:

The correct dropdown option is: angle JMG is congruent to angle KMH

The completed proof logic confirms $JG = KH$ as required.