Step-by-step explanation:
Before we start, let's look at what we're trying to prove: that two triangles are congruent. There are a few ways we can do that: SSS, SAS, ASA, or AAS. Whichever we choose, we'll need to show that at least one pair of sides is congruent. We can do that, since we know that H is the midpoint of LM. So we'll either use ASA or AAS.
1. LG || JM, H is the midpoint of LM
Given
2. LH ≅ HM
Definition of midpoint
3. ∠GLH ≅ ∠JMH
Alternate interior angles theorem
(∠GLH and ∠JMH are alternate interior angles. Since LG and JM are parallel, the alternate interior angles are congruent.)
4. ∠LHG ≅ ∠MHJ
Vertical angles theorem
(∠LHG and ∠MHJ are vertical angles, which are always congruent.)
5. ΔLGH ≅ ΔMJH
ASA
(We have two pairs of congruent angles, and a pair of congruent sides between them.)
Now, I chose to use ASA. However, you could use AAS. Instead of using vertical angles in step 4, we could have used alternate interior angles theorem to show that ∠LGH ≅ ∠MJH.
