Question

given (overline{jk} parallel overline{lm}), (overline{jk} cong overline{lm}),
l is the midpoint of (overline{jn}).
prove: (\triangle jlk cong \triangle lnm)

statements

1. l is the midpoint of (overline{jn}) 1. given
2. (overline{jk} cong overline{lm}) 2. given

blank given

the statement is part of this proof,
but at least one other statement must
come before it.

Explanation:

Step1: Identify the third given

We know we need to prove \(\triangle JLK \cong \triangle LNM\) using SAS. We have \(L\) is the midpoint (so \(JL = LN\)) and \(\overline{JK} \cong \overline{LM}\). The third part for SAS (angle between the sides) comes from \( \overline{JK} \parallel \overline{LM}\), so \(\angle J=\angle NLM\) (corresponding angles). So the next statement (third given - related) is \(\overline{JK} \parallel \overline{LM}\).

Step2: Fill the statement

In the proof table, the next statement (with reason "given") should be \(\overline{JK} \parallel \overline{LM}\).

Answer:

The missing statement (to be filled in the proof table) is \(\boldsymbol{\overline{JK} \parallel \overline{LM}}\)