Chapter 6, Section 1 Polygons

Describing a Polygon An enclosed figure (all segments) Two segments a point called a vertex Each segment is called a side.

Identifying a Polygon Number of Sides n Type of Polygon Type of polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n-gon

Convex & Concave Polygon Convex Polygon Normal shapes that you are used to seeing everyday Example: street signs Concave Polygon One side is bent into the polygon or outside the polygon. Example: a star

Chapter 6, Section 2 Properties of Parallelograms

Definition of a Parallelogram A quadrilateral where both pairs of opposite side are parallel.

Theorems about Parallelograms If both pairs of opposite sides of a quadrilateral are congruent. If both pairs of opposite angles of a quadrilateral are congruent. If an angle of a quadrilateral is supplementary to both consecutive angles. If the diagonals of a quadrilateral bisect each other.

Chapter 6, Section 3 Proving Quadrilaterals are Parallelograms

Theorems Proving the Quadrilateral is a Parallelogram If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If an angle of a quadrilateral is supplementary to both consecutive angles, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If one pair of opposite sides of a quadrilateral are congruent & parallel, then the quadrilateral is a parallelogram.

Chapter 6, Section 4 Rhombuses, Rectangles & Squares

Rhombus Is a parallelogram w/ four congruent sides.

Rectangle Is a parallelogram w/ four right angles.

Square Is a parallelogram w/ four congruent sides & four right angles.

Diagonals A parallelogram is a rhombus if and only if the diagonals are perpendicular. A parallelogram is a rhombus if and only if the diagonals bisect a pair of opposite angles. A parallelogram is a rectangle if and only if its diagonals are congruent.

Chapter 6, Section 5 Trapezoids & Kites

Trapezoid Has exactly one pair of parallel sides. The parallel sides are called the bases. The other two sides are called the legs. In an Isosceles Trapezoid the legs are congruent.

Theorems of a Trapezoid If a trapezoid is isosceles, then each pair of base angles are congruent. If a trapezoid has a pair of congruent base angles, then its an isosceles trapezoid. A trapezoid is isosceles if and only if its diagonals are congruent.

Midsegment

Kite Is a quadrilateral that has two pairs of consecutive congruent sides. The diagonals are perpendicular. Has exactly one pair of opposite angles which are congruent.

Chapter 6, Section 6 Special Quadrilaterals

Draw flow chart of Quadrilaterals

Chapter 6, Section 7 Areas of Triangles & Quadrilaterals

Area Figure 1 Square 2 Rectangle 3 Parallelogram 4 Triangle 5 Trapezoid 6 Kite 7 Rhombus Formula

Area of Irregular Shapes Break the figure into familiar polygons. Find the area of each & then find the sum of the areas.