Question

example
(1) decide if the figure drawn below is a rhombus. explain your reasoning.
yes, the figure drawn is a rhombus. it is a parallelogram with one pair of consecutive sides congruent.

Explanation:

Identify the properties of the given figure

Using the Parallelogram Theorems knowledge point

• Opposite sides \(KL\) and \(JM\) are parallel, indicated by double arrows (\(\gg\)).
• Opposite sides \(JK\) and \(LM\) are parallel, indicated by single arrows (\(>\)).
• Therefore, quadrilateral \(JKLM\) is a parallelogram.

Analyze the side markings

Using the Rhombus Properties and Rhombus Definition knowledge points

• Side \(KL\) and side \(JK\) each have a single tick mark, showing \(KL \cong JK\).
• These are consecutive sides of the parallelogram.
• A parallelogram with at least one pair of congruent consecutive sides is a rhombus.

Formulate the final conclusion

Using the Rhombus Definition knowledge point

• Since \(JKLM\) is a parallelogram with congruent consecutive sides \(KL \cong JK\), all four sides are congruent.
• Thus, the figure is a rhombus.

Answer:

Yes, the figure drawn is a rhombus. It is a parallelogram with one pair of consecutive sides congruent, which means all four sides are congruent.