Ming wanted to travel with her Mandarin class to Beijing for spring break.

Although her parents gave Ming permission to go on the trip, they didn't have the money to pay for it, and she could go only if she earned the money to pay for it herself. First, Ming considered getting a part-time job after school.

But the trip was too expensive to earn enough money that way. Then, she discovered a design competition. The winner of the competition would receive a cash prize that was just enough to pay for the trip! Ming knew she was at a disadvantage because she was a 10th grader, and she'd compete against high school juniors and seniors. Nevertheless, she didn't let that stop her.

Ming read the competition rules: Design and create three figures. Figure #1 should have a general set of properties. Figure #2 must be distinct from Figure #1 but still have all the properties of Figure #1. Figure #3 must be distinct from #1 and #2 but still have all the properties of both. At first, Ming was at a loss, but then she remembered something she recently learned in her geometry class...

Ming decided to create a set of lanterns. She knew how to make each lantern distinct but fulfill the contest design rules. Her first lantern was shaped like a convex quadrilateral. What are the properties of a convex quadrilateral? A convex quadrilateral has: 4 straight sides 4 vertices all interior angles less than or equal to 180° Ming's next lantern was shaped like a parallelogram. A parallelogram has all the properties of a convex quadrilateral. However, it's distinct because it has additional properties. What are the additional properties of a parallelogram? The parallelogram is a convex quadrilateral with: parallel opposite sides congruent opposite angles supplementary adjacent angles For her third figure, Ming designed and created a lantern shaped like a rhombus. The rhombus is a parallelogram with a few additional properties. What are the properties of the rhombus? The rhombus is a parallelogram with four congruent sides. Ming's lantern collection impressed the judges. She had created three figures that met all the competition criteria. The convex quadrilateral had a set of general properties. The parallelogram was a distinct quadrilateral, and the rhombus was a distinct parallelogram. Furthermore, her lanterns were beautiful. Ming won the competition, and she looked forward to celebrating in Beijing!

Ming recognized that the rhombus has all the properties of a convex quadrilateral and a parallelogram. However, the rhombus has distinct properties of its own and is, therefore, the subject of this lesson.