Question

using the sas congruence theorem
given: jk || lm, jk ≅ lm,
l is the mid - point of jn.
prove: △jlk ≅ △lnm
statements reasons

1. jk || lm 1. given

Explanation:

Step1: Identify equal - side from mid - point

Since L is the mid - point of JN, we have JL = LN (by the definition of mid - point).

Step2: Identify equal angles

Because JK || LM, ∠J = ∠NLM (by the corresponding angles theorem).

Step3: Identify the other equal side

We are given that JK = LM.

Step4: Apply SAS congruence

In △JLK and △LNM, we have JL = LN (side), ∠J = ∠NLM (angle), and JK = LM (side). So, △JLK ≅ △LNM by the SAS (Side - Angle - Side) congruence theorem.

Answer:

Statements: 2. JL = LN; 3. ∠J = ∠NLM; 4. △JLK ≅ △LNM
Reasons: 2. def. of midpoint; 3. corresponding angles theorem; 4. SAS