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 (\boldsymbol{checkmark}) by the definition of a midpoint. it is also given that angles jgm and khm are right angles. thus, 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 (\boldsymbol{\text{?}}) criteria. in congruent triangles, correspon congruent angles.
(the drop - down options are: segment gm is congruent to segment km; segment jm is congruent to segment hm; segment gm is congruent to segment hm; segment jm is congruent to segment km)

Explanation:

Step1: Identify midpoint segment congruence

By definition of midpoint, $GM \cong HM$

Step2: Note right angle congruence

All right angles are congruent, so $\angle JGM \cong \angle KHM$

Step3: Identify vertical angle congruence

Vertical angles are congruent, so $\angle JMG \cong \angle KMH$

Step4: Apply triangle congruence criteria

Using ASA (Angle-Side-Angle) criteria, $\triangle JMG \cong \triangle KMH$

Step5: Corresponding parts of congruent triangles

Corresponding sides of congruent triangles are congruent, so $JG=KH$

Answer:

First dropdown: segment GM is congruent to segment HM
Second dropdown: ASA