High School

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Given:

- \( jk \parallel lm \)
- \( jk = lm \)
- \( l \) is the midpoint of \( jn \)

a) \( \overline{ca} \) bisects \(\angle bad\)
b) \( \overline{ab} \perp bc \)
c) \( \overline{ad} \perp dc \)
d) Statement 2

Answer :

Final answer:

This involves using Congruence theorems. It has been proved that; JKL ≅ LNM

Explanation:

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

Learn more about Geometry here:

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