Question

given: ( \triangle kjl cong \triangle nml ) n is the midpoint of ( overline{mo} ). prove: kjon is a parallelogram. 7. ( overline{kj} parallel overline{no} ) 7. 8. 8.

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle KJL\cong\triangle NML\), we have \(KJ = NM\) (corresponding parts of congruent triangles are equal).

Step2: Use the mid - point property

Because \(N\) is the mid - point of \(MO\), \(NM=NO\). Then \(KJ = NO\) (by substitution).

Step3: Use the definition of a parallelogram

A quadrilateral with one pair of opposite sides parallel (\(\overline{KJ}\parallel\overline{NO}\)) and equal (\(KJ = NO\)) is a parallelogram.

Answer:

1. If two triangles are congruent, their corresponding sides are equal. Also, mid - point divides a line segment into two equal parts.
2. \(KJ = NO\); A quadrilateral with one pair of opposite sides parallel and equal is a parallelogram.