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, angle jmg is congruent to angle kmh because all right angles are congruent. since vertical angles are congruent by the vertical angles theorem. then, it follows that (\triangle jmgcong\triangle kmh) by the criteria. in congruent triangles, correspond kh. in conclusion (jg = kh) by definition of congruent angles.
(the drop - down options are: angle mjg is congruent to angle mkh; angle jmg is congruent to angle khm; angle jmg is congruent to angle kmh; angle jgm is congruent to angle khm))

Explanation:

Step1: Identify midpoint congruence

$GM \cong HM$ (definition of midpoint)

Step2: Identify right angle congruence

$\angle JGM \cong \angle KHM$ (all right angles are congruent)

Step3: Identify vertical angle congruence

$\angle JMG \cong \angle KMH$ (vertical angles theorem)

Step4: Prove triangle congruence

$\triangle JMG \cong \triangle KMH$ (ASA congruence criteria)

Step5: Corresponding parts are congruent

$JG = KH$ (CPCTC: congruent triangles have congruent corresponding sides)

Answer:

1. segment GM is congruent to segment HM
2. angle JGM is congruent to angle KHM
3. angle JMG is congruent to angle KMH
4. ASA (Angle-Side-Angle)
5. $JG = KH$