2PolygonsA Polygon is a closed plane figure with three or more straight sides.examples:The siluette of that house is a polygon because it is a closed figure with no curved lines.
3The parts of a polygon are: -sides: each segments -vertices: are the common endpoints of two points-diagonals: segment that connects any two nonconsecutive vertices.vertexsidevertexdiagonaldiagonaldiagonalsidesidevertex
4A convex polygon is a polygon in which all vertices are pointing out. Examples:
5A concave polygon is a figure that has one or more vertices pointing in. Examples:
6Equilateral is when all the sides of the polyogon are congruuent.
7Equiangular is when all the angles of a polygon are congruent.
8Interior Angle Theorem for Polygons: The number of sides minus two and then multiplied times 180 will tell you the sum of the interior angles.12 – 2 = 1010 x 180 = 1800Sum of the interior angles = 1800°5 – 2 = 33 x 180 = 540Sum of the interior angles = 540 °examples:3 – 2 = 11 x 180 = 180Sum of the interior angles = 180°1800°540°180°
94 theorems of parallelograms and its converse: Theorem 6-2-1: If a quadrilateral is a parallelogram,then its opposite sides are congruentConverse: If a quadrilateral has its opposite sides that are congruent, then it is a parallelogram.
10Theorem 6-2-2: If a quadrilateral is a parallelogram,then its opposite angles are congruent. Converse: If a quadrilateral has opposite angles that are congruent, then it is a parallelogram
11Theorem 6-2-3: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Converse: If a quadrilateral has consecutive angles that are supplementary, then it is a parallelogram.80100
12Theorem 6-2-4: If a quadrilateral is a parallelogram, then its diagonals bisect each other. Converse: If a quadrilateral has diagonals that bisect eachother, then it is a parallelogram.
13How to prove that a quadrilateral is a parallelogram. To know that a quadrilateral is a parallelogram, we have to know the six characteristics of a parallelogram:Opposite sides are congruent.Opposite angles are congruent.Consecutive angles are supplementary.Diagonals bisect eachother.One set of cogruent and parallel sides.Definition: quadrilateral that has opposite sides parallel to eachother
14Examples:Yes, parallelogram.We don’t have enough information to tell if it’s a parallelogram.Yes, becuse the diagonals bisect eachother.
15Rhombus + square + rectangle Rhombus: It has 4 congruent sides and diagonals are perpendicular.
16Square: It is equiangular and equilateral, it is both a rectangle and a rhombus and its diagonals are congruent and perpendicular.
17Rectangle: Diagonals are congruent and has four right angles. These three figures have in common that they are all parallelograms and have four sides.
18Trapezoid and its theorems A trapezoid is quadrilateral with one pair of parallel sides, each of the parallel sides is called a base and the nonparallel sides are called legs.Baselegs
19Theorems:6-6-3: if a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.6-6-4: if a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles.6-6-5: a trapezoid is isosceles if and only if its diagonals are congruent
20KiteA kite is a quadrilateral that has 2 pairs of congruent adjacent sides (2 lines at the top are congruent and the 2 lines at the bottom are congruent)The properties:Diagonals are perpendicularOne of the diagonals bisect the otherOne pair of congruent angles (the ones formed by the non-congruent sides)
21Kite Theorems:6-6-1: if a quadrirateral is a kite, then its diagonals are perpendicular.6-6-2: if a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.