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8.5 Trapezoids and Kites

8.5 Trapezoids and Kites. Goal 1 Using Properties of Trapezoids Goal 2 Using Properties of Kites. Using Properties of Trapezoids. A Trapezoid is a quadrilateral with exactly one pair of parallel sides. Trapezoid Terminology The parallel sides are called BASES .  

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8.5 Trapezoids and Kites

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  1. 8.5 Trapezoids and Kites Goal 1 Using Properties of Trapezoids Goal 2 Using Properties of Kites

  2. Using Properties of Trapezoids A Trapezoid is a quadrilateral with exactly one pair of parallel sides. • Trapezoid Terminology • The parallel sides are called BASES.   • The nonparallel sides are called LEGS.  • There are two pairs of base angles, the two touching the top base, and the two touching the bottom base.

  3. Using Properties of Trapezoids ISOSCELES TRAPEZOID - If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid. Theorem- Both pairs of base angles of an isosceles trapezoid are congruent. Theorem– If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. Theorem- The diagonals of an isosceles trapezoid are congruent.

  4. Using Properties of Trapezoids Example 1 CDEF is an isosceles trapezoid with leg CD = 10 and mE = 95°. Find EF, mC, mD, and mF.

  5. Using Properties of Trapezoids Area of trapezoid = When working with a trapezoid, the height may be measured anywhere between the two bases.  Also, beware of "extra" information.  The 35 and 28 are not needed to compute this area. Find the area of this trapezoid. A = ½ * 26 * (20 + 42) A = 806

  6. Using Properties of Trapezoids Example 2 Find the area of a trapezoid with bases of 10 in and 14 in, and a height of 5 in.

  7. Using Properties of Trapezoids Midsegment of a Trapezoid – segment that connects the midpoints of the legs of the trapezoid.

  8. Using Properties of Trapezoids Theorem: Midsegment Theorem for Trapezoids The midsegment of a trapezoid is parallel to each base and its length is one-half the sum of the lengths of the bases.

  9. Using Properties of Trapezoids Example 4 Find AB, mA, and mC

  10. Using Properties of Trapezoids Example 5

  11. Using Properties of Kites

  12. Using Properties of Kites A quadrilateral is a kite if and only if it has two distinct pair of consecutive sides congruent. • The vertices shared by the congruent sides are ends. • The line containing the ends of a kite is a symmetry line for a kite. • The symmetry line for a kite bisects the angles at the ends of the kite. • The symmetry diagonal of a kite is a perpendicular bisector of the other diagonal.

  13. Using Properties of Kites Theorem If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. mB = mC

  14. Using Properties of Kites Area Kite = one-half product of diagonals

  15. Using Properties of Kites Example 6 ABCD is a Kite. a) Find the lengths of all the sides. 2 4 4 E 4 • Find the area of the Kite.

  16. Using Properties of Kites Example 7 A CBDE is a Kite. Find AC.

  17. Using Properties of Kites Example 8 ABCD is a kite. Find the mA, mC, mD

  18. Areas of Triangles and Quadrilaterals

  19. Area Formulas (Copy diagrams from page 372) • Area of a Rectangle: The area of a rectangle is the product of its base and height. • A = bh • Area of a Parallelogram: The area of a parallelogram is the product of a base and its corresponding height. • A = bh • Area of a Triangle: The area of a triangle is one half the product of a base and its corresponding height. • A = ½ bh

  20. Area formulas (Copy formulas from page 374) • Area of a Trapezoid: The area of a trapezoid is one half the product of the height and the sum of the bases. • A = ½ h(b1 + b2) • Area of a Kite: The area of a kite is one half the product of the length of its diagonals. • A = ½ d1d2 • Area of a Rhombus: The area of a rhombus is equal to one half the product of the lengths of the diagonals. • A = ½ d1d2

  21. Homework/Classwork

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