![]() ![]() Kites are a special type of quadrilateral with two distinct pairs of consecutive sides the same length. Likewise, every square is also a rectangle, because a rectangle has 4 right angles, but every rectangle is not a square. Similarly, every square is also a rhombus, because all four sides are the same length, but every rhombus is not a square. ![]() For example, every square is also a parallelogram, because both pairs of its opposite sides are equal, but every parallelogram is not a square. These definitions exist in a hierarchy of relationships. A rectangle has 4 right angles, and a square has four equal sides and four right angles. A rhombus is a type of quadrilateral with all sides the same length. Each has its own special features.Ī quadrilateral is a parallelogram if both pairs of its opposite sides are parallel. Types of quadrilaterals often overlap, so that a figure that fits in one category may also fit in another. There are seven different types of quadrilaterals: parallelogram, rhombus, rectangle, square, kite, trapezoid, and isosceles trapezoid. They are classified according to measures of equal angles and equal sides. And if I’m going to get there, I can’t do everything else.Ī week after this lesson, students successfully worked through the Floor Plan.Īnd so, whether or not we have the best plan, the journey continues….Quadrilaterals are polygons with four sides. I’m not convinced that full-time modeling is the way to go in my classes yet, but I want to get to modeling. ![]() We proved those properties – and then we observed properties of other quadrilaterals that were already constructed. Instead, my students constructed the parallelogram from the definition. But I’ve decided I’m not going to spend the time that it takes to do that. I think it would be great to have time for my students to construct every one of the quadrilaterals according to their definition and then observe the resulting properties. One teacher thought that students should construct the kite instead of it already being made. I’ve had conversations with teachers about some of the Geometry Nspired documents giving away too much of the math. But I still want to provide my students the opportunity to think about the structure of a kite while they’re not alone on an assessment. I get why kites aren’t explicitly listed in the standards but might still show up in the tasks. Since the kite is two isosceles triangles, we can deduce even more properties. Some students noticed that diagonal IG decomposes the kite into two isosceles triangles. ![]() Some students noticed that diagonal KN is a line of reflection for the two triangles that it creates. Then I sent a Quick Poll to assess what they had observed. I gave students about three minutes to play with with this page. We used the Math Nspired activity Rhombi_Kites_and_Trapezoids as a guide for our exploration. So they enjoyed thinking about a figure that was mostly new to them. And my students haven’t thought about properties of kites before. And the Mathematics Assessment Project task Floor Plan has kites in it. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.īut look for and make use of structure is one of the Standards for Mathematical Practice. So kites aren’t specifically listed in CCSS-M. ![]()
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