Lesson 8.5: Properties of Trapezoids and Kites Geometry

Definitions Trapezoid: A Quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases. The nonparallel sides are the legs. A Trapezoid has two pairs of base angles. The first pair are the angles that are adjacent to the bottom base. The second pair are the angles adjacent to the top base.

Example Points A, B, C and D are the vertices of a quadrilateral. Determine whether ABCD is a trapezoid

Check For Progress Points A, B, C and D are the vertices of a quadrilateral. Determine whether ABCD is a trapezoid

Definitions Isosceles Trapezoid: A trapezoid in which the legs are congruent to one another. Each pair of base angles is congruent. The diagonals are congruent to one another.

Example Find the measure of all angles.

Check For Progress Find the measure of all angles.

Definitions Midsegment Theorem for Trapezoids: The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

Example Find the length of the midsegment of the trapezoid.

Check For Progress Find the length of the midsegment of the trapezoid.

Definitions Kite: A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent. Diagonals are perpendicular to one another. Exactly one pair of opposite angles are congruent to one another.

Example KITE is a kite. Find the measure of angle K.

Example Find the side lengths of the kite. Write the lengths in simplest radical form.

Check For Progress Find the side lengths of the kite. Write the lengths in simplest radical form.

Homework Workbook Pg. 157 #1-16 (all)