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6.5 Trapezoid and Kites

6.5 Trapezoid and Kites. Which of these sums is equal to a negative number? (4) + (-7) + (6) (-7) + (-4) (-4) + (7) (4) + (7). In the first seven games of the basketball season, Cindy scored 8, 2, 12, 6, 8, 4 and 9 points. What was her mean number of points scored per game? 6 7 8 9.

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6.5 Trapezoid and Kites

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  1. 6.5 Trapezoid and Kites

  2. Which of these sums is equal to a negative number? (4) + (-7) + (6) (-7) + (-4) (-4) + (7) (4) + (7) In the first seven games of the basketball season, Cindy scored 8, 2, 12, 6, 8, 4 and 9 points. What was her mean number of points scored per game? 6 7 8 9 Warmup

  3. Let’s define Trapezoid base A B > leg leg > C D base <D AND <C ARE ONE PAIR OF BASE ANGLES. When the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

  4. Isosceles Trapezoid • If a trapezoid is isosceles, then each pair of base angles is congruent. B A D C

  5. PQRS is an isosceles trapezoid. Find m<P, m<Q, and m<R. S R > 50° > P Q

  6. Isosceles Trapezoid • A trapezoid is isosceles if and only if its diagonals are congruent. B A D C

  7. Midsegment Theorem for Trapezoid • The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the base. C B N M A D

  8. Examples • The midsegment of the trapezoid is RT. Find the value of x. 7 R x T x = ½ (7 + 14) x = ½ (21) x = 21/2 14

  9. Examples • The midsegment of the trapezoid is ST. Find the value of x. 8 S 11 T 11 = ½ (8 + x) 22 = 8 + x 14 = x x

  10. Review In a rectangle ABCD, if AB = 7x – 3, and CD = 4x + 9, then x = ___ A) 1 B) 2 C) 3 D) 4 E) 5 7x – 3 = 4x + 9 -4x -4x 3x – 3 = 9 + 3 +3 3x = 12 x = 4

  11. Kite • A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are congruent.

  12. Theorems about Kites • If a quadrilateral is a kite, then its diagonals are perpendicular • If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. B A C L D

  13. Example • Find m<G and m<J. J Since m<G = m<J, 2(m<G) + 132° + 60° = 360° 2(m<G) + 192° = 360° 2(m<G) = 168° m<G = 84° H 132° 60° K G

  14. Example • Find the side length. J 12 H K 12 14 12 G

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