6.2.3 Properties of Kites and Trapezoids (continued)
The perimeter of a kite is determined in this application example. The following lengths are given: AE = CE = 12 inches, BE = 7 inches, and DE = 20 inches. Since the figure is a kite, the diagonals are perpendicular and form right triangles with their hypotenuses forming the sides of the kite. The length of AB is calculated using the Pythagorean Theorem to be 193 inches. By the definition of a kite, AB ≅ BC . So BC is also equal to 193 inches. The length of CD is calculated using the Pythagorean Theorem to be 4 34 inches. By the definition of a kite, this is also the length of AD . The perimeter of the kite is the sum of the four sides, which can be approximated using a calculator to be 74.4 inches. Since each package of binding contains 24 inches, 4 packages are needed to completely cover the perimeter.
Example 2 Using Properties of Kites
This is a property of a kite. If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
The measure of an angle in a kite, PQRS , is determined in this example. The measures of ∠ RQW and ∠ RSW are given. By the properties of kites, the diagonals are perpendicular, so m ∠ RWS = 90°. Since the acute angles of a right triangle are complementary, m ∠ WRS + m ∠ RSW = 90°. Substituting the given 20° for m ∠ RSW yields m ∠ WRS = 70°.
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