TechMathI - 5.1 - Polygons

Bell Ringer

Welcome to Welcome to the World the World

of of Polygons!Polygons!

PolygonsPolygons

The word polygon means The word polygon means “many angles”“many angles”

A two dimensional objectA two dimensional object A closed figureA closed figure

More about More about PolygonsPolygons

Made up of three or more Made up of three or more straight line segmentsstraight line segments

There are exactly two sides There are exactly two sides that meet at a vertexthat meet at a vertex

The sides do not cross The sides do not cross each othereach other

Vocabulary

• Diagonal – a line segment joining 2 non-consecutive vertices

• Adjacent – ‘next to’

Examples of PolygonsExamples of Polygons

These are not These are not PolygonsPolygons

Terms:Terms:

Side: One of the line Side: One of the line segments that make up segments that make up a polygon.a polygon.

Vertex: point where two Vertex: point where two sides meet.sides meet.

Regular Polygon: Regular Polygon: a polygon where all the a polygon where all the

angles are equal and all of angles are equal and all of the sides are the same the sides are the same length. length.

Examples of Regular Examples of Regular PolygonsPolygons

Types of Types of PolygonsPolygons

TriangleTriangle A triangle has three sides.A triangle has three sides.

1

2

3

Everyday triangles…Everyday triangles…

There are There are several types several types of trianglesof triangles

Isosceles Triangles Isosceles Triangles have 2 equal sides.have 2 equal sides.

Equilateral Equilateral Triangles have 3 Triangles have 3 equal sidesequal sides

Scalene Scalene Triangles have Triangles have no equal sidesno equal sides

Acute triangles Acute triangles have 3 acute have 3 acute anglesangles

Obtuse triangles Obtuse triangles have 1 obtuse have 1 obtuse angleangle

Right triangles have Right triangles have 1 right angle1 right angle

Quadrilateral Quadrilateral A quadrilateral has four sides.A quadrilateral has four sides.

SquareSquare

Squares have 4 equal parallel sides Squares have 4 equal parallel sides and 4 right angles.and 4 right angles.

Squares are regular polygonsSquares are regular polygons

Everyday SquaresEveryday Squares

RectanglesRectangles

Rectangles have parallel sides that Rectangles have parallel sides that are equal to each other.are equal to each other.

All angles are right angles.All angles are right angles.

Everyday RectanglesEveryday Rectangles

RhombusRhombus A rhombus has four equal parallel sides.A rhombus has four equal parallel sides.

ParallelogramParallelogram

Parallelograms have opposite equal Parallelograms have opposite equal parallel sidesparallel sides

Everyday ParallelogramsEveryday Parallelograms

TrapezoidTrapezoid

Trapezoids have one set of Trapezoids have one set of parallel sides.parallel sides.

Everyday TrapezoidsEveryday Trapezoids

PentagonPentagon A pentagon has five sides.A pentagon has five sides.

1

2

3

4

5

Everyday PentagonsEveryday Pentagons

Hexagon Hexagon

A hexagon has six sides. (Hexagon A hexagon has six sides. (Hexagon and six both have an “x”.)and six both have an “x”.)

Everyday HexagonsEveryday Hexagons

HeptagonHeptagon

A heptagon has seven sides.A heptagon has seven sides.

Everyday HeptagonsEveryday Heptagons

OctagonOctagon

An octagon has eight sides. An octagon has eight sides.

What does this remind you of?

Everyday OctagonsEveryday Octagons

NonagonsNonagons

Nonagons have nine sidesNonagons have nine sides

Everyday NonagonsEveryday Nonagons

DecagonDecagon Decagons have 10 sides.Decagons have 10 sides.

Everyday DecagonsEveryday Decagons

HendecagonHendecagon

Hendecagons have 11 Hendecagons have 11 sidessides

Everyday HendecagonsEveryday Hendecagons

DodecagonsDodecagons

Dodecagons have 12 sidesDodecagons have 12 sides

Everyday DodecagonsEveryday Dodecagons

A triangle is the smallest polygon because it has three sides. Can you have a two-sided polygon? Why or why not?

Two lines don’t close to make a shape. They make an angle.

2

1

Key Question:Key Question:

Name all diagonals with an endpoint at vertex C.

Name all angles adjacent to A.

Name the polygon.

Name all diagonals with an endpoint at vertex B.

Name all angles not adjacent to D.

Name the polygon.

You try!

3x

2x+1

The perimeter of the parallelogram is 42 inches. Find length of the base.

2x + 2

4x - 2

The perimeter of the parallelogram is 84 feet. Find length of the base.

You try!