Objectives Use properties of kites to solve problems. Use properties of trapezoids to solve problems.

_____________ – a quadrilateral with exactly two pairs of congruent consecutive sides.

Example 1: Problem-Solving Application Lucy is framing a kite with wooden dowels. She uses two dowels that measure 18 cm, one dowel that measures 30 cm, and two dowels that measure 27 cm. To complete the kite, she needs a dowel to place along . She has a dowel that is 36 cm long. About how much wood will she have left after cutting the last dowel?

Understand the Problem Example 1 Continued 1 Understand the Problem The answer will be the amount of wood Lucy has left after cutting the dowel. 2 Make a Plan The diagonals of a kite are perpendicular, so the four triangles are right triangles. Let N represent the intersection of the diagonals. Use the Pythagorean Theorem and the properties of kites to find , and . Add these lengths to find the length of .

Example 1 Continued Solve 3

Example 2A: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mBCD.

Example 2B: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mABC.

Example 2C: Using Properties of Kites In kite ABCD, mDAB = 54°, and mCDF = 52°. Find mFDA.

__________ – a quadrilateral with exactly one pair of parallel sides. __________ – Each of the parallel sides. __________ – The nonparallel sides. __________– two consecutive angles of a trapezoid whose common side is a base. __________________– a trapezoid that has two congruent legs.

Theorem 6-6-5 is a biconditional statement Theorem 6-6-5 is a biconditional statement. So it is true both “forward” and “backward.” Reading Math

Example 3A: Using Properties of Isosceles Trapezoids Find mA.

Example 3B: Using Properties of Isosceles Trapezoids KB = 21.9 and MF = 32.7. Find FB.

Example 4A: Applying Conditions for Isosceles Trapezoids Find the value of a so that PQRS is isosceles.

Example 4B: Applying Conditions for Isosceles Trapezoids AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.

_____________________– the segment whose endpoints are the midpoints of the legs. In Lesson 5-1, you studied the Triangle Midsegment Theorem. The Trapezoid Midsegment Theorem is similar to it.

Example 5: Finding Lengths Using Midsegments Find EF.