Glencoe Geometry Chapter 6

Diagonal

• A diagonal connects nonconsecutive vertices in a polygon.

Polygon Interior Angle Sum Theorem 6.1

• For an n-sided convex polygon, the sum of interior angles is calculated as (n-2)×180 degrees.

Polygon Exterior Angles Sum Theorem 6.2

• The sum of the exterior angles of a convex polygon, one angle at each vertex, equals 360 degrees.

Parallelogram

• A quadrilateral with parallel opposite sides; any side may serve as the base.

Properties of Parallelograms 6.3

• Opposite sides of a parallelogram are congruent.

Properties of Parallelograms 6.4

• Opposite angles of a parallelogram are congruent.

Properties of Parallelograms 6.5

• Consecutive angles of a parallelogram are supplementary.

Properties of Parallelograms 6.6

• If one angle of a parallelogram is a right angle, all angles are right angles.

Properties of Parallelograms 6.7

• Diagonals of a parallelogram bisect each other.

Properties of Parallelograms 6.8

• Each diagonal of a parallelogram separates it into two congruent triangles.

Conditions for Parallelograms 6.9

• A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

Conditions for Parallelograms 6.10

• A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

Conditions for Parallelograms 6.11

• A quadrilateral is a parallelogram if its diagonals bisect each other.

Conditions for Parallelograms 6.12

• A quadrilateral is a parallelogram if one pair of opposite sides is both parallel and congruent.

Rectangle

• A quadrilateral with four right angles.

Diagonals in a Rectangle 6.13

• In rectangles, diagonals are congruent.

Diagonals in a Rectangle 6.14

• If diagonals of a parallelogram are congruent, it is a rectangle.

Rhombus

• A quadrilateral with all sides congruent.

Square

• A quadrilateral with four right angles and four congruent sides.

Diagonals of a Rhombus 6.15

• Diagonals of a rhombus are perpendicular to each other.

Diagonals of a Rhombus 6.16

• Each diagonal of a rhombus bisects a pair of opposite angles.

Conditions for Rhombi and Squares 6.17

• A parallelogram with perpendicular diagonals is a rhombus.

Conditions for Rhombi and Squares 6.18

• If a diagonal of a parallelogram bisects a pair of opposite angles, it is a rhombus.

Conditions for Rhombi and Squares 6.19

• A parallelogram is a rhombus if one pair of consecutive sides is congruent.

Conditions for Rhombi and Squares 6.20

• A quadrilateral that is both a rectangle and a rhombus is a square.

Trapezoid

• A quadrilateral with exactly one pair of parallel sides.

Bases

• The parallel sides of a trapezoid are called the bases.

Legs of a Trapezoid

• The nonparallel sides of a trapezoid are known as the legs.

Base Angle

• Formed by a base and one of the legs in a trapezoid.

Isosceles Trapezoid

• A trapezoid where the legs are congruent.

Mid Segment of a Trapezoid

• Connects the midpoints of the legs; parallel to the bases.

Kite

• A quadrilateral with two pairs of adjacent congruent sides.

Isosceles Trapezoid 6.21

• In an isosceles trapezoid, each pair of base angles is congruent.

Isosceles Trapezoid 6.22

• A trapezoid with one pair of congruent bases is isosceles.

Isosceles Trapezoid 6.23

• A trapezoid is isosceles if and only if its diagonals are congruent.

Trapezoid Midsegment Theorem 6.24

• The midsegment is parallel to the bases and measures half the sum of the lengths of the bases.

Kites 6.25

• The diagonals of a kite are perpendicular.

Kites 6.26

• In a kite, exactly one pair of opposite angles is congruent.