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**An Introduction to Quadrilaterals**

by Carol Edelstein

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**Polygon – a closed, straight-sided, plane figure.**

Definition Polygon – a closed, straight-sided, plane figure.

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**Angle – two rays that meet at a common end point.**

Definition Angle – two rays that meet at a common end point.

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Definition Degree – a unit of measurement of an angle, represented by the symbol º. 90º

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Definition Diagonal – a line segment joining two non-adjacent vertices of a polygon.

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**Quadrilateral – a polygon with 4 angles and 4 straight sides.**

Definition Quadrilateral – a polygon with 4 angles and 4 straight sides.

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**Special Quadrilaterals**

Parallelograms – opposite sides are parallel and congruent. Rectangles – a parallelogram with all angles 90°. Squares – a rectangle with all sides equal . Rhombus – a parallelogram with all sides equal. Trapezoid – one set of sides are parallel.

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**Venn Diagram Persective of Quadrilaterals**

Quadrilaterals – 4 sided polygon Parallelograms (opposite sides are parallel and congruent). Trapezoids (one set of parallel sides) Rhombus Rectangle Square

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**Quadrilateral Family trapezoid parallelogram rectangle rhombus**

square

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**Property of Quadrilaterals**

The sum of all the interior angles equals 360º.

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**Property of Quadrilaterals**

Why is the sum 360º ? Well, if you choose a vertex you can only draw one diagonal. This one diagonal “splits” the quadrilateral into two triangles. Since the sum of the internal angles of a triangle are 180 degrees, a quadrilateral has 360 degrees (2 x 180 º ).

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**Property of Quadrilaterals**

The sum of all the interior angles equals 360º degrees. 65º 65º 115º 65º 115º 115º + 65º 115º 360º

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**What is the missing angle?**

90º 90º 90º 90º 90º + 90º ? 90º ? 360º

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**What is the missing angle?**

70º 70º 70º 70º 110º ? 110º 110º ? + 360º

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**What is the missing angle?**

65º 65º ? 65º 115º 65º 115º 115º + ? 360º

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**What is the missing angle?**

60º 81º 104º ? 104º 115º 60º 81º + ? 360º

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**Congratulations and good job!**

Now you know that… A quadrilateral is a 4-sided polygon. There are many types of quadrilaterals. Classification depends on how many sets of sides are parallel, the length of the sides and the measure of the interior angles. The sum of the interior angles of a quadrilateral is 360º.

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Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 9.2 Polygons.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 9.2 Polygons.

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