*Polygons

Polygons*These figures are not polygonsThese figures are polygonsDefinition:A closed figure formed by line segments so that each segment intersects exactly two others, but only at their endpoints.

Classifications of a Polygon*Convex:No line containing a side of the polygon contains a point in its interiorConcave:A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.

Classifications of a Polygon*Regular:A convex polygon in which all interior angles have the same measure and all sides are the same lengthIrregular:Two sides (or two interior angles) are not congruent.

Polygon Names*3 sidesTriangle4 sides5 sides6 sides7 sides8 sidesNonagonOctagonHeptagonHexagonPentagonQuadrilateral10 sides9 sides12 sidesDecagonDodecagonn sidesn-gon

Regular PolygonsRegular polygons have:All side lengths congruentAll angles congruent*

Area of Regular PolygonApothem of a polygon: the distance from the center to any side of the polygon.*

Area of Regular PolygonWe can now subdivide the polygon into triangles.

*

Triangles and Quadrilaterals*

Lesson 3-4: Polygons

Classifying Triangles by SidesEquilateral:*Scalene:A triangle in which all 3 sides are different lengths.Isosceles:A triangle in which at least 2 sides are equal.A triangle in which all 3 sides are equal.AB = 3.02 cmAC = 3.15 cmAB = 3.47 cmAC = 3.47 cmGH = 3.70 cmGI = 3.70 cm

Classifying Triangles by AnglesA triangle in which all 3 angles are less than 90.*Acute:Obtuse:A triangle in which one and only one angle is greater than 90& less than 180

Classifying Triangles by Angles*Right:Equiangular:A triangle in which one and only one angle is 90A triangle in which all 3 angles are the same measure.

*Classification by Sides with Flow Charts & Venn Diagrams Scalene Equilateral Isosceles Triangle Polygon

*Classification by Angles with Flow Charts & Venn Diagrams Right Equiangular Acute Triangle Polygon Obtuse

What is a Quadrilateral?All quadrilaterals have four sides. They also have four angles. The sum of the four angles totals 360These properties are what make quadrilaterals alike, but what makes them different?

Lesson 3-4: Polygons

ParallelogramTwo sets of parallel sides Two sets of congruent sides.The angles that are opposite each other are congruent (equal measure).

Rectangle Has all properties of quadrilateral and parallelogram

A rectangle also has four right angles.

A rectangle can be referred to as an equiangular parallelogram because all four of its angle are right, meaning they are all 90 (four equal angles).

RhombusA rhombus is sometimes referred to as a slanted square.A rhombus has all the properties of a quadrilateral and all the properties of a parallelogram, in addition to other properties.A rhombus is often referred to as a equilateral parallelogram, because it has four sides that are congruent (each side length has equal measure).

SquareThe square is the most specific member of the family of quadrilaterals. The square has the largest number of properties.

Squares have all the properties of a quadrilateral, all the properties of a parallelogram, all the properties of a rectangle, and all the properties of a rhombus.

A square can be called a rectangle, rhombus, or a parallelogram because it has all of the properties specific to those figures.

Lesson 3-4: Polygons

TrapezoidUnlike a parallelogram, rectangle, rhombus, and square who all have two sets of parallel sides, a trapezoid only has one set of parallel sides. These parallel sides are opposite one another. The other set of sides are non parallel.

Isosceles TrapezoidOne can never assume a trapezoid is isosceles unless they are given that the trapezoid has specific properties of an isosceles trapezoid.

Isosceles is defined as having two equal sides. Therefore, an isosceles trapezoid has two equal sides. These equal sides are called the legs of the trapezoid, which are the non-parallel sides of the trapezoid.

Both pair of base angles in an isosceles trapezoid are also congruent.

Right TrapezoidA right trapezoid also has one set of parallel sides, and one set of non-parallel sides.

A right trapezoid has exactly two right angles. This means that two angles measure 90.

There should be no problem identifying this quadrilateral correctly, because its just like its name. When you think of right trapezoid, think of right angles!

Quadrilateral Family TreeIts important to have a good understanding of how each of the quadrilaterals relate to one another.

Any quadrilateral that has two sets of parallel sides can be considered a parallelogram.

A rectangle and rhombus are both types of parallelograms, and a square can be considered a rectangle, rhombus, and a parallelogram.

Any quadrilateral that has one set of parallel sides is a trapezoid. Isosceles and Right are two types of trapezoids.

QuadrilateralParallelogramTrapezoidRectangleRhombusSquareIsoscelesTrapezoid

RightTrapezoid

*********