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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