The same is true for the angle measures of angle ??? and angle ???. Because we have these two congruent triangles, we know that the measure of angle ??? will be equal to the measure of angle ???. The other two triangles at the bases are similar. The diagonals of an isosceles trapezoid create two congruent triangles at the legs. The diagonal property tells us that if an angle created by a diagonal and side is equal in measure to the angle created by the other diagonal and opposite side, then the quadrilateral is cyclic. We can use the angle properties in a quadrilateral to help us determine if it’s cyclic or not. We then need to establish if isosceles trapezoids are cyclic quadrilaterals, that is, a quadrilateral which has all four vertices inscribed on a circle. In the figure below, if we take the line segments ?? and ?? to be parallel, then that means that ???? is an isosceles trapezoid. An isosceles trapezoid is a special type of trapezoid that has the additional property that the two nonparallel sides or legs are equal in length. Let’s begin by recalling that a trapezoid is a quadrilateral with one pair of parallel sides. M ∠ ABC = 120°, because the base angles of an isosceles trapezoid are equal.īD = 8, because diagonals of an isosceles trapezoid are equal.įigure 5 A trapezoid with its two bases given and the median to be computed.True or False: All isosceles trapezoids are cyclic quadrilaterals. In trapezoid ABCD (Figure 3) with bases AB and CD , E the midpoint of AD , and F the midpoint of BC , by Theorem 55:Įxample 1: In Figure 4, find m ∠ ABC and find BD.įigure 4 An isosceles trapezoid with a specified angle and a specified diagonal. (2) Its length equals half the sum of the base lengths. Theorem 55: The median of any trapezoid has two properties: (1) It is parallel to both bases. Recall that the median of a trapezoid is a segment that joins the midpoints of the nonparallel sides.
Slopes: Parallel and Perpendicular Lines.
Special Features of Isosceles Triangles.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.