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Quadrilateral Lesson

Quadrilateral Lesson. There are seven major types of quadrilaterals: parallelogram, rhombus, rectangle, square, kite, trapezoid, and isosceles trapezoid. Definition: A quadrilateral is a parallelogram if and only if its opposite sides are parallel. B. C. A. D.

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Quadrilateral Lesson

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  1. Quadrilateral Lesson There are seven major types of quadrilaterals: parallelogram, rhombus, rectangle, square, kite, trapezoid, and isosceles trapezoid.

  2. Definition: A quadrilateral is a parallelogram if and only if its opposite sides are parallel. B C A D AB CD, BC AD

  3. Definition: A quadrilateral is a rhombus if and only if its four sides are equal in length. E F H G EF = FG = GH = HE

  4. Definition: A quadrilateral is a rectangle if and only if it has four right angles. J K I L I, J, K, L are right angles.

  5. Definition: A quadrilateral is a square if and only if it has four equal sides and four right angles. M N P O MN = NO = OP = PM M, N, O, P are right angles.

  6. From the definitions, one can see that every square is a rhombus, since every square has four equal sides. One can also conclude that every square is a rectangle, since every square has four right angles. This information is summarized in the network below. This network shows a part of a hierarchy of quadrilaterals. rectangle rhombus square

  7. Because two perpendiculars to the same line are parallel, every rectangle is a parallelogram. As a result, “parallelogram” can be added to the hierarchy. B C A D parallelogram rhombus rectangle square

  8. A fifth type of quadrilateral is formed by the union of two isosceles triangles having the same base, with the base re- moved. The result is a quadrilateral that resembles a kite or arrowhead. Pictured here is the convex kite ABCD. B A C AB = BC AD = DC D

  9. Definition: A quadrilateral is a kite if and only if it has two distinct pairs of consecutive sides of the same length. B A C AB = BC AD = DC D

  10. From the definitions of kite and rhombus, one can conclude that every rhombus is a kite. This information is added to the hierarchy. One can now conclude that every square is a kite by reading up the hierarchy from square to rhombus to kite. kite parallelogram rectangle rhombus square

  11. Definition: A quadrilateral is a trapezoid if and only if it has at least one pair of parallel sides. T R TR PA P A Parallel sides of a trapezoid are called bases. In the figure above, TR and PA are bases. Two consecutive angles that share a base are called base angles. This terminology enables the class to de- fine a special type of trapezoid.

  12. Definition: A trapezoid is isosceles if and only if it has a pair of base angles equal in measure. A B isosceles trapezoid with bases AB and CD D C AB DC, m D = m C

  13. Because a rectangle has opposite sides parallel and all angles equal, every rectangle is an isosceles trapezoid. You can now relate all these seven types of quadrilaterals in the same hierarchy. This is shown by the dark lines below. quadrilateral kite trapezoid isosceles trapezoid parallelogram rhombus rectangle square

  14. The hierarchy of quadrilaterals is very useful because it allows properties of some quadrilaterals to apply to other quadrilaterals. The general rule is: ANY property held by a type of figure in the hierarchy is also held by all the types of figures below it to which it is connected. For example, square is below rhombus in the hierarchy. Thus, any square has all the properties of a rhombus. Squares and rhombuses are below kite. Thus, they have all the properties of kites.

  15. For further assessment: - Look at students’ note page. - Look at quadrilateral worksheet page. (Both of these documents may be linked from the “Main Lesson Page”)

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