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Understanding Trapezoids and Kites: Concepts, Formulas, and Example Problems

Explore the intricacies of trapezoids and kites in this comprehensive guide. Learn the characteristics that define trapezoids, including isosceles trapezoids and their properties, such as congruent legs and base angles. Gain insights on calculating the midsegment of a trapezoid, utilizing important theorems, and solving example problems. Additionally, discover the properties of kites, focusing on their unique side lengths and angle relationships. This resource combines definitions, theorems, and practical examples to enhance your understanding of these geometric shapes.

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Understanding Trapezoids and Kites: Concepts, Formulas, and Example Problems

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  1. 6.5 Trapezoid and Kites Day 5

  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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