Answer:
1. Given
2. Alternate interior angle theorem
3. Alternate interior angle theorem
4. Reflexive property of congruence
5. ASA
Step-by-step explanation:
1. JK || LM, JL || KM
This is the information given in the problem statement.
2. ∠JKL ≅ ∠MLK
∠JKL and ∠MLK are alternate interior angles. Since JK and LM are parallel, the alternate interior angles are congruent.
3. ∠JLK ≅ ∠MKK
∠JLK and ∠MKL are alternate interior angles. Since JL and KM are parallel, the alternate interior angles are congruent.
4. KL ≅ LK
According to reflexive property, a segment is always congruent to itself.
5. ΔJKL ≅ ΔMLK
We have two triangles with two pairs of congruent angles, and a pair of congruent sides between those angles. Therefore, the triangles are congruent by ASA.
