Chapter 8.5 Notes: Use Properties of Trapezoids and Kites

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Presentation transcript:

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. The nonparallel sides are the legs of the trapezoid.

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

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.

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

Ex. 3: The top of the table in the diagram is an isosceles trapezoid 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.

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 = __________________________

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.

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

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.

Ex. 7: Find in the kite shown below. Ex 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.

Ex.9: Find in the kite shown.