8.5 – Use Properties of Trapezoids and Kites

Trapezoid: Consecutive interior angles are supplementary A B C D m  A + m  D = 180° m  B + m  C = 180° Quadrilateral with one pair of opposite sides parallel base leg

Isosceles Trapezoid: The nonparallel sides of the trapezoid are congruent

Isosceles Trapezoid: The base angles are congruent The diagonals are congruent A B CD

Midsegment of a Trapezoid: The midsegment is half the sum of the parallel sides A B CD F E

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

Kite: Exactly one pair of opposite angles are  Its diagonals are perpendicular

Find the m  B, m  C, m  D. 53° m  B = 53° = m  C = 127° m  D =

Find the m  B, m  C, m  D = m  B = m  C = 83° 97° m  D = 83°

Find the length of the midsegment.

Find x. 8 = 4x 2 = x 1

Find x. x = 4 1 7x = 28

Given the isosceles trapezoid, find x and all base angles. 1 80° 100°

Determine whether the quadrilateral is a trapezoid. If it is, is it an isosceles trapezoid? Yes, it is a trapezoid Alternate interior angles are , so one pair of parallel lines No

Determine whether the quadrilateral is a trapezoid. If it is, is it an isosceles trapezoid? No, No parallel lines

Determine whether the quadrilateral is a trapezoid. If it is, is it an isosceles trapezoid? Yes, Base angles are congruent Isosceles trapezoid

WEST is a kite. Find the missing angles x x = 360 2x = 360 2x = 236 x = 118° x x

WEST is a kite. Find the missing angles. x x + 88 = 360 x = 360 x = 77° 88°

HW Problem , 8-11, 13, 15, 19-21, odd #20, SKIP # 21 Ans: x + x = 360 x = 60° xx