#18 y + 8 = 3y #28 2y = 10 #32 #38 #48 (On next slide) Checkpoint 8.4 p.537 (Properties of Rhombuses, Rectangles, and Squares) #18 - all sides are  - opposite ’s  - diagonals are  - diagonals bisects interior angles - opposite sides are parallel y + 8 = 3y 8 = 2y 4 = y 180 – 104 = x 76 = x #28 2y = 10 y = 5 3x + 18 = 5x 18 = 2x 9 = x #32 #38 #48 (On next slide)

= 53 = 90 - 34 = 56 = MK + KP = 1 + 1 = 2

Section 8.5 – Use Properties of Trapezoids and Kites Geometry Section 8.5 – Use Properties of Trapezoids and Kites I find the misegment of a trapezoid to find the midsegment or base I can use the properties of quadrilateral to set up and solve equations to find variables

A trapezoid is a quadrilateral with at least one pair of parallel lines

= base1 + base2 2

EXAMPLE 3 Use the midsegment of a trapezoid In the diagram, MN is the midsegment of trapezoid PQRS. Find MN. ANSWER The length MN is 20 inches.

EXAMPLE 2 Use properties of isosceles trapezoids Arch The stone above the arch in the diagram is an isosceles trapezoid. Find m K, m M, and m J.

EXAMPLE 4 Apply Theorem 8.19 Find m D in the kite shown at the right.

Example 4 Find the Missing angles in each Kite a) b)