Question

for any rhombus jklm, decide whether the statement \\(\overrightarrow{jl}\cong \overrightarrow{km}\\) is always or sometimes true. this statement is sometimes true. explain your reasoning. a some rhombuses are squares. b each diagonal of a rhombus bisects a pair of opposite angles. c by definition, a rhombus is a parallelogram with four congruent sides. d by definition, a rhombus is a parallelogram, and opposite sides of a parallelogram are congruent.

Explanation:

A rhombus is defined as a parallelogram with four congruent sides. In any parallelogram, opposite sides are congruent, so for rhombus $JKLM$, $\overline{JL}$ and $\overline{KM}$ are its diagonals. The diagonals of a rhombus are only congruent when the rhombus is a square (a special case of a rhombus). For non-square rhombuses, the diagonals are not congruent. Thus, the statement is only true in some cases.

Answer:

This statement is sometimes true.