') made by swapping the 'if' and 'then' parts of another statement. 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. Definition of Converse (logic) A conditional statement ('if. (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. By Theorem 53, m ∠ DAB = m ∠ CBA, and m ∠ ADC = m ∠ BCD.įigure 2 An isosceles trapezoid with its diagonals.In isosceles trapezoid ABCD (Figure 2) with bases AB and CD : Theorem 54: Diagonals of an isosceles trapezoid are equal. Theorem 53: Base angles of an isosceles trapezoid are equal.

In Figure 1, ∠ A and ∠ B or ∠ C and ∠ D are base angles of trapezoid ABCD. Two special properties of an isosceles trapezoid can be proven. If the legs of a trapezoid are equal, it is called an isosceles trapezoid. Figure is an isosceles trapezoid.Ī pair of angles that share the same base are called base angles of the trapezoid. Recall that a trapezoid is a quadrilateral with only one pair of opposite sides parallel and that the parallel sides are called bases and the nonparallel sides are called legs. Summary of Coordinate Geometry Formulas.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.

Converse geometry definition diagram