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Unit 6 Lesson 4 Use Properties of Trapezoids and Kites

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 °. base. A. B. m  B + m  C = 180 °. leg. leg. D. C. base.

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Unit 6 Lesson 4 Use Properties of Trapezoids and Kites

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  1. Unit 6 Lesson 4Use Properties of Trapezoids and Kites

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

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

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

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

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

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

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

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

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

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

  12. 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

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

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

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

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

  17. HW Problem #20 x + x + 150 + 90 = 360 x x 2x + 240 = 360 2x = 120 x = 60°

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