Sect. 6.5 Trapezoids and Kites Goal 1 Using Properties of Trapezoids Goal 2 Using Properties of Kites

Trapezoid definition A Trapezoid is a quadrilateral with only one pair of parallel sides.

Using Properties of Trapezoids 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.

Using Properties of Trapezoids ISOSCELES TRAPEZOID - If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid. Theorem - Both pairs of base angles of an isosceles trapezoid are congruent. Theorem - The diagonals of an isosceles trapezoid are congruent. Theorem – If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Using Properties of Trapezoids Midsegment of a Trapezoid – segment that connects the midpoints of the legs of the trapezoid.

Using Properties of Trapezoids Theorem: 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.

Using Properties of Kites

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 symmetry diagonal of a kite is a perpendicular bisector of the other diagonal. 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.

Using Properties of Kites Theorem: If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. m  B = m  C

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

Using Properties of Kites Example 7 CBDE is a Kite. Find AC. A

Using Properties of Kites Example 8 ABCD is a kite. Find the m  A, m  C, m  D