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Properties of Trapezoids and Kites: Theorems and Examples

Explore the characteristics of trapezoids and kites, including midsegments, isosceles properties, and angle calculations through practical examples. Learn to identify trapezoids and determine if they are isosceles. Practice finding missing angles in kites.

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Properties of Trapezoids and Kites: Theorems and Examples

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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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