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**2-12-15 Polygons and Quadrilaterals Unit**

Trapezoids and Kites

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**Flow Chart Quadrilaterals Parallelogram Rectangle Rhombus Square**

Non Parallelograms Parallelogram Rhombus Rectangle Trapezoid Kite Square Isosceles Trapezoid

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**Trapezoid Definition:**

A quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases and the non-parallel sides are called legs. Trapezoid Base Leg An Isosceles trapezoid is a trapezoid with congruent legs. Isosceles trapezoid

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**A Trapezoid is a quadrilateral with exactly one pair of parallel sides.**

Trapezoid Terminology The parallel sides are called BASES. The nonparallel sides are called LEGS. There are two pairs of base angles, the two touching the top base, and the two touching the bottom base.

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**Properties of Isosceles Trapezoid**

1. Both pairs of base angles of an isosceles trapezoid are congruent. 2. The diagonals of an isosceles trapezoid are congruent. B A Base Angles D C

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ISOSCELES TRAPEZOID - If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid. **** - Both pairs of base angles of an isosceles trapezoid are congruent. **** - The diagonals of an isosceles trapezoid are congruent.

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Example 1 CDEF is an isosceles trapezoid with leg CD = 10 and mE = 95°. Find EF, mC, mD, and mF.

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**Find the area of this trapezoid.**

When working with a trapezoid, the height may be measured anywhere between the two bases. Also, beware of "extra" information. The 35 and 28 are not needed to compute this area. Area of trapezoid = Find the area of this trapezoid. A = ½ * 26 * ( ) A = 806

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Example 2 Find the area of a trapezoid with bases of 10 in and 14 in, and a height of 5 in.

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Median of a Trapezoid The median of a trapezoid is the segment that joins the midpoints of the legs. The median of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases. Median

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**Midsegment of a Trapezoid – segment that connects the midpoints of the legs of the trapezoid.**

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**Midsegment Theorem for Trapezoids**

The midsegment of a trapezoid is parallel to each base and its length is one-half the sum of the lengths of the bases.

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Example 2 Find AB, mA, and mC

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Example 3

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**A quadrilateral is a kite if and only if it has two distinct pair of consecutive sides congruent.**

The vertices shared by the congruent sides are ends. The line containing the ends of a kite is a symmetry line for a kite. The symmetry line for a kite bisects the angles at the ends of the kite. The symmetry diagonal of a kite is a perpendicular bisector of the other diagonal.

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**Using Properties of Kites**

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. mB = mC

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**Area Kite = one-half product of diagonals**

Using Properties of Kites Area Kite = one-half product of diagonals

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**a) Find the lengths of all the sides.**

Using Properties of Kites Example 3 ABCD is a Kite. a) Find the lengths of all the sides. 2 4 4 E 9 Find the area of the Kite.

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**Using Properties of Kites**

Example 4 A CBDE is a Kite. Find AC.

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**ABCD is a kite. Find the mA, mC, mD**

Using Properties of Kites Example 5 ABCD is a kite. Find the mA, mC, mD

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