6.2.3 Properties of Kites and Trapezoids (continued)
This is a property of an isosceles trapezoid. A trapezoid is isosceles if and only if its diagonals are congruent. Since this is a biconditional statement, it is true in both directions. The measure of an angle in an isosceles trapezoid, ABCD , is determined in this example. The figure is given to be an isosceles trapezoid and the measure of ∠ DAB is given. It is also given that AB || DC and AD ≅ BC . Since AB || DC , m ∠ A + m ∠ D = 180° by the Same- Side Interior Angles Theorem. Substitute the given value for m ∠ A and solve to find m ∠ D = 60°. By the Properties of Isosceles Trapezoids, ∠ C ≅ ∠ D and therefore m ∠ C = m ∠ D = 60°. The length of half of a diagonal in an isosceles trapezoid, ABCD , is determined in this example. The figure is given to be an isosceles trapezoid. It is given that the diagonal AC has length 12.7 units, and BE has length 7.1 units. It is also given that AD || BC and AB ≅ DC . Because this is an isosceles trapezoid, the diagonals are congruent, and therefore BD = 12.7 by the definition of congruent line segments. By the Segment Addition Postulate, BE + ED = BD . Substituting gives 7.1 + ED = 12.7. Solving gives ED = 5.6.
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