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Chapter 8.5 Notes: Use Properties of Trapezoids and Kites

Chapter 8.5 Notes: Use Properties of Trapezoids and Kites. Goal: You will use properties of trapezoids and kites. Trapezoids A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases . A trapezoid has two pairs of base angles .

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Chapter 8.5 Notes: Use Properties of Trapezoids and Kites

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  1. Chapter 8.5 Notes: Use Properties of Trapezoids and Kites Goal: You will use properties of trapezoids and kites.

  2. Trapezoids • A trapezoid is a quadrilateral with exactly one pair of parallel sides. • The parallel sides are called the bases. • A trapezoid has two pairs of base angles. • The nonparallel sides are the legs of the trapezoid.

  3. Ex.1: Show that ORST is a trapezoid. • If the legs of a trapezoid are congruent, then the trapezoid is an isosceles trapezoid.

  4. Theorem 8.14: If a trapezoid is isosceles, then each pair of base angles are congruent. • Theorem 8.15: If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. • Theorem 8.16: A trapezoid is isosceles if and only if its diagonals are congruent.

  5. Ex.2: The stone above the arch in the diagram is an isosceles trapezoid. Find

  6. Ex.3: The top of the table in the diagram is an isosceles trapezoid. Find • The midsegment of a trapezoid is the segment that connects the midpoints of its legs.

  7. Theorem 8.17 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. Midsegment = __________________________

  8. Ex.4: In the diagram, is the midsegment of trapezoid PQRS. Find MN. Ex.5: In the diagram, is the midsegment of trapezoid DEFG. Find HK.

  9. Ex.6: Use the diagram of trapezoid EFGH. • If EG = FH, is trapezoid EFGH isosceles? Explain. • If and , is trapezoid EFGH isosceles? Explain.

  10. Kites • A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent. • Theorem 8.18: If a quadrilateral is a kite, then its diagonals are perpendicular. • Theorem 8.19: If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

  11. Ex.7: Find in the kite shown below. Ex.8: In a kite, the measures of the angles are 3xo, 75o, 90o, and 120o. Find the value of x. What are the measures of the angles that are congruent.

  12. Ex.9: Find in the kite shown.

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