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Understanding Trapezoids and Kites: Definitions, Properties, and Theorems

This resource provides a comprehensive overview of trapezoids and kites, including their definitions, properties, and theorems. A trapezoid is a quadrilateral with one pair of parallel sides, while a kite has two pairs of congruent consecutive sides. Key theorems are highlighted, such as properties of isosceles trapezoids, relationships between angles, and characteristics of kites. The material includes examples, ensuring a clear understanding of how to identify and apply the properties of these unique quadrilaterals in geometry.

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Understanding Trapezoids and Kites: Definitions, Properties, and Theorems

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  1. Trapezoids and Kites

  2. Definition Trapezoid • A quadrilateral with exactly one pair of parallel sides • Bases: the parallel sides • Legs: the non-parallel sides • Isosceles: when the legs are congruent base1 A B leg leg D C base2

  3. Definition Trapezoid • A quadrilateral with exactly one pair of parallel sides • Bases: the parallel sides • Legs: the non-parallel sides W leg X base1 base2 Z leg Y

  4. Definition Kite A quadrilateral with two pairs of congruent consecutive sides. F E G H

  5. Definition Kite A quadrilateral with two pairs of congruent consecutive sides. Q P S R

  6. Theorem If a trapezoid is isosceles, then each pair of base angles is congruent. A B D C

  7. Theorem If a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid. A B D C

  8. Theorem A trapezoid is isosceles if and only if its diagonals are congruent. A B D C

  9. Theorem The midsegment of a trapezoid is parallel to each base and its length isthe average of the lengths of the bases. A B E F D C

  10. Theorem The diagonals of a kite are perpendicular. A D B C

  11. Theorem The angles between the non-congruent sides of a kite are congruent. B A D C

  12. Example 1 CDEF is an isosceles trapezoid. C D CE = 10 95o F E

  13. Example 2 PQRS is a trapezoid with the given measurements. 8 Q P 110o 85o N M R S 10

  14. Example 2 Continued PQRS is a trapezoid with the given measurements. 8 Q P 110o 85o N M R S 10

  15. Example 2 Continued PQRS is a trapezoid with the given measurements. 8 Q P 110o 85o N M R S 10

  16. Example 3 HIJK is a kite. Find HP H 2 5 I L P J

  17. Example 4 DEFG is a kite. D 70o x + 30 E 125o 125o G 40o x F

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