Middle School

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Using the SAS Congruence Theorem

Given:
- \( JK \parallel LM \)
- \( JK \cong LM \)
- \( L \) is the midpoint of \( JN \)

Prove:
\[ \triangle JKL \cong \triangle LNM \]

Answer :

This involves using Congruence theorems.

It has been proved that; JKL ≅ LNM

The image of the two triangles is missing and so I have attached it.

We are told that;

  • 1) JK || LM ; This means that Line JK is parallel to Line LM.

  • 2) JK ≅ LM ; This means that Line JK is Congruent to Line LM. Two congruent lines means they are equal. Thus; JK = LM.


  • 3) L is the midpoint of JN; As seen in the attached image that point L is at the middle of Line JN.


  • 4) From point 3 above, we can deduce that; LN = JL

This is because the midpoint of a line bisects the line into 2 equal parts.


  • 5) From the attached image, we can say that; ∠LJK = ∠NLM. This is because they are corresponding angles since from the Corresponding angles theorem, when a transverse cuts across two parallel lines, the corresponding angles are congruent.


  • 6.) Since, we have 2 corresponding sides to have equal length and the included angle for both triangles is equal, then by SAS Congruence theorem, we can say that both triangles are congruent;

△JLK ≅ △LNM

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Rewritten by : Barada

Answer + Step-by-step explanation:

Given: JK || LM, JK≅ LM

L is the midpoint of JN

Prove: △JLK ≅△LNM