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6.5 Trapezoids & Kites

6.5 Trapezoids & Kites. Trapezoid. Is a quadrilateral with exactly 1 pair of parallel sides. BASE. base angle. base angle. leg. leg. base angle. base angle. BASE. Trapezoid. A B. C D. If the legs are congruent then the trapezoid is an isosceles trapezoid. Theorem 6.14.

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6.5 Trapezoids & Kites

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  1. 6.5Trapezoids & 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

  18. Add Trapezoid and Kite to your foldable.

  19. 5.4 Midsegment Theorem Goal: Identify midsegments and use properties of midsegments of a triangle

  20. Midsegment – a segment that connects the midpoints of two sides of a triangle.

  21. MidsegmentTheorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long. B X Y AC || XY XY = ½ AC A C

  22. Ex 1: UW and VW are midsegments of RST. Find UW and RT. R U UW = 6 V 12 8 RT = 16 T W S

  23. Ex 2: X, Y, and Z are the midpoints of UVW. Complete each statement. • If VW = 6a, then XY = ___ • b. mWZY = 2b + 1, then mWVU = ______. • c. XZ  _______. • d. If YZ = c, then UV = ____ U X Y W V Z

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