+

8.5 Use Properties of Trapezoids and Kites

+Trapezoid: quadrilateral with exactly one pair of parallel sides.

Two pairs of base angles: A and D & B and C

**Find the slopes of RS and OT. Are they the same? If so, they are parallel.

Slope of RS: 1/2Slope of OR: 1/2

Angle K = 85Angle M and J are congruent because it’s isosceles.M = J = 95

+Midsegment of a trapezoid: segment that connects the midpoints of the legs

+

MN = (28 + 12)/2 = 40/2 = 20

3. yes, the diagonals are congruent4. Yes, EFG is 70 by consecutive interior angles

J K

LM

N P

9cm

12 cm

90

90

To find ML : (9 + x) / 2 = 12ML = x = 15

x

+Kite: Quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent

+

Since angle E and G are not congruent, D and F must be congruent.

2x + 124 + 80 = 360Angle D = Angle F = X = 78

3x + 75 + 90 + 120 = 360

X = 2575 degrees is the measure of the angles that are congruent

Find the missing side lengths. Leave your answers in simplest radical form

+P. 546 (3-27, odd)