Unit 6 Lesson 4 Use Properties of Trapezoids

Unit 6 Lesson 4 Use Properties of Trapezoids and Kites

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

Midsegment of a Trapezoid: • Connects the midpoints of the legs of a trapezoid base midsegment = base + base 2

Isosceles Trapezoid: • Nonparallel sides of the trapezoid are congruent • The base angles are congruent • The diagonals are congruent B A D C

Kite: Quadrilateral that has two pairs of consecutive congruent sides • Exactly one pair of opposite angles are • Its diagonals are perpendicular

1. Find the m B, m C, m D. 53° 127°

1. Find the m B, m C, m D. 83° 97° 83°

2. Find the length of the midsegment. 20 7 + 13 base + base = = 10 midsegment = = 2 2 2

2. Find the length of the midsegment. 22 + 18 40 base + base = = 20 midsegment = = 2 2 2

3. Find x. 1 8 = 4 x 2=x

3. Find x. 1 7 x = 28 x=4

4. 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

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

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

5. WEST is a kite. Find the missing angles. 29 + x + 95 + x = 360 x x 2 x + 124 = 360 2 x = 236 x = 118°

5. WEST is a kite. Find the missing angles. 107 + 88 + x + 88 = 360 88° x x + 283 = 360 x = 77°

HW Problem LT Assignment Due 6. 1, 6. 2 1, 8 -11, 13, 15, 19, 20, 25 -29 odd #20 x x x + 150 + 90 = 360 2 x + 240 = 360 2 x = 120 x = 60°