Sect 6 5 Trapezoids and Kites Goal 1

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 – If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. Theorem - The diagonals of an isosceles trapezoid are congruent.

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

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 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.

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