Objective: To verify and use properties of trapezoids and kites.

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Presentation transcript:

Objective: To verify and use properties of trapezoids and kites. Chapter 6 Lesson 5 Objective: To verify and use properties of trapezoids and kites.

Trapezoids

The parallel sides of a trapezoid are its bases The parallel sides of a trapezoid are its bases. The nonparallel sides are its legs. Two angles that share a base of a trapezoid are base angles of the trapezoid.

The base angles of an isosceles trapezoid are congruent. Theorem 6-15 The base angles of an isosceles trapezoid are congruent. The bases of a trapezoid are parallel. Therefore the two angles that share a leg are supplementary.

Example 1: Finding Angles Measures ABCD is an isosceles trapezoid and m B = 102. Find m A, m C, and m D. By Theorem 6-15, m C = m B = 102 and m D = m A = 78.

Example 2: Finding Angles Measures In the isosceles trapezoid, m S = 70. Find m P, m Q, and m R. By Theorem 6-15, m S = m R= 70 and m P = m Q = 110.

The diagonals of an isosceles trapezoid are congruent. Theorem 6-16 The diagonals of an isosceles trapezoid are congruent.

Kites

The diagonals of a kite are perpendicular. Theorem 6-17 The diagonals of a kite are perpendicular.

Example 3: Finding Angles Measures Find m 1, m 2, and m 3 in the kite. by SSS By CPCTC, m 3 = m DBC = 32

Example 4: Finding Angles Measures Find m 1, m 2, and m 3 in the kite.

Assignment Pg. 322 #1-37