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Understanding Trapezoids and Kites: Properties and Theorems

This guide explains the characteristics of trapezoids and kites, including definitions, properties, and related theorems. A trapezoid is a quadrilateral with one pair of parallel sides. It can be classified as isosceles if its legs are congruent, and its base angles are congruent. The midsegment connects the midpoints of the legs and is parallel to the bases. A kite features two pairs of consecutive congruent sides and has perpendicular diagonals. The guide also includes examples for calculating lengths and angles of trapezoids and kites.

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Understanding Trapezoids and Kites: Properties and Theorems

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  1. Trapezoids & Kites

  2. Trapezoid • Is a quadrilateral with exactly 1 pair of parallel sides

  3. BASE base angle base angle leg leg base angle base angle BASE Trapezoid A B C D

  4. If the legs are congruent then the trapezoid is an isosceles trapezoid.

  5. Theorem 6.14 • If a trapezoid is isosceles, then each pair of base angles is congruent.

  6. Theorem 6.15 • If a trapezoid has a pair of congruent base angles, then it isan isosceles trapezoid.

  7. Theorem 6.16 • A trapezoid is isosceles if and only if its diagonals are congruent.

  8. Midsegment • The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

  9. THM 6.17 • The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of its bases

  10. EX 1 Find the length of MN. 10 16 P Q 13 M N S R

  11. EX 2 Find the value of x. 19 15 17 x

  12. A Kite • A quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent.

  13. Theorem 6.18 • If a quadrilateral is a kite, then its diagonals are perpendicular.

  14. Theorem 6.19 • If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

  15. Ex 3 Find the measure of the sides. Round to the nearest tenth. LM = 3.6 LO = 3.6 ON= 5 MN = 5 L 2 O M 3 3 4 N

  16. Ex 4 Find the mL. 110 L M 100 40 O N

  17. Ex 5 Find the mL. 35 L M x 55 O 135 N

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