and
Kites
Study Guides
Big Picture Not all quadrilaterals are parallelograms. Trapezoids and kites are two non-parallelograms with special properties.
Key Terms Trapezoid: Quadrilateral with exactly one pair of parallel sides. Isosceles Trapezoid: A trapezoid where the non-parallel sides are congruent.
Geometry
Trapezoids
Midsegment: A line segment that connects the midpoints of the non-parallel sides of a trapezoid. Kite: Quadrilateral with two sets of adjacent congruent sides.
Trapezoids The parallel sides of a trapezoid are called the bases, while the nonparallel sides are called the legs. A pair of angles that share the same base are called base angles. A trapezoid has two sets of base angles.
Isosceles Trapezoids
Think of an isosceles trapezoid as an isosceles triangle with the top cut off. As result, many of the theorems that describe isosceles triangles have corresponding theorems for trapezlids. The properties of isosceles trapezoids are defined by the following theorems: Theorem: Both pairs of base angles of an isosceles trapezoid are congruent.
• The converse can also be used: If a trapezoid has congruent base angles, then it is an isosceles trapezoid. Theorem: The diagonals of an isosceles trapezoid are congruent.
Midsegments The midsegment is parallel to the bases and is located halfway between them.
• If EF is the midsegment of trapezoid ABCD, then EF || AB, EF || DC, and This guide was created by Nicole Crawford, Jane Li, Amy Shen, and Zachary Wilson. To learn more about the student authors, visit http://www.ck12.org/ about/about-us/team/interns.
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Disclaimer: this study guide was not created to replace your textbook and is for classroom or individual use only.
Theorem: The length of the midsegment of a trapezoid is the average of the lengths of the bases.
Geometry
Trapezoids
and
Kites
cont .
Kites A kite has two sets of adjacent, distinct congruent sides. Rhombuses and squares are not kites! Kites can be concave. A concave kite (the rightmost kite in the diagram below) is called a dart.
When working with kites, think of the traditional kites that are flown in the air.
The angles between the congruent sides are called vertex angles. The other angles are non-vertex angles.
Theorem: The non-vertex angles of a kite are congruent. Theorem: The diagonal through the vertex angles is the angle bisector for both angles. Kite Diagonals Theorem: The diagonals of a kite are perpendicular.
•  If KITE is a kite, then
Notes
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