Geometry Notes Lesson 4.2A Properties of Special Quadrilaterals R.4.G.1 Explore and verify the properties of quadrilaterals

Trapezoids  Definition:  Bases:  Legs: A quadrilateral with exactly one pair of parallel sides The parallel sides The non parallel sides

Trapezoids  Median of a Trapezoid : The segment that joins the midpoints of the legs median leg base leg B A C D

Trapezoids  Pairs of Base Angles:  Supplementary Angles median leg base leg B A C D Located along the same base Adjacent angles not along the same base

Isosceles Trapezoid  Both pairs of base angles of an isosceles trapezoid are congruent

Isosceles Trapezoid  The diagonals of an isosceles trapezoid are congruent

Isosceles Trapezoid  The median of a trapezoid is parallel to the bases and measures ½ of the sum of the bases Median =

Kites  Definition: A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent

Kites  The diagonals of a kite are perpendicular.

Kites  Segment DE  Segment BE  1  2  3  4  ABC  ADC B A D C E

Example #1 Find the value of the numbered angles.  Find the sum of the angles.  Formula: 180(n-2)  The angles between the noncongruent sides are equal in measure.  Let angles 1 and 2 both be x. 53 o 47 o 1 2

Example #1 Find the value of the numbered angles.  Find the sum of the angles.  Formula: 180(n-2)  Opposite angles are congruent.  Adjacent angles are supplementary. 50 o 1 2

Example #2 Find the value of the variable.  The diagonals of a kite are perpendicular.  All four triangles in the kite are right triangles.  The sum of the angles in a triangle are 180°. (4x + 9) o (2x+3) o

Example #2 Find the value of the variable  Adjacent angles are supplementary. (3x) o (2x) o