Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface...

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Geometry: Part 2 Geometry: Part 2 3-D figures 3-D figures

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Transcript of Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface...

Page 1: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

Geometry: Part 2Geometry: Part 2

3-D figures3-D figures

Page 2: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

PolyhedronPolyhedron

►3-dimensional analog of a polygon3-dimensional analog of a polygon►Closed surface made up of polygonsClosed surface made up of polygons►Any 2 polygons may have only one Any 2 polygons may have only one

shared edgeshared edge

Face

EdgeVertex

Page 3: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

PrismPrism

► Polyhedron with 2 opposite faces that Polyhedron with 2 opposite faces that are identical polygonsare identical polygons

►Faces are called basesFaces are called bases

►Bases are joined by lateral faces Bases are joined by lateral faces If the lateral face is a rectangle it is a If the lateral face is a rectangle it is a right right

prismprism

Page 4: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

Examples:Examples:

► 2 hexagons for 2 hexagons for basesbases

► Right Hexagonal Right Hexagonal prismprism

► 2 rectangles for 2 rectangles for basesbases

► Right rectangular Right rectangular prismprism

base

Lateral face

Page 5: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

Geometry in the Real World Geometry in the Real World

Page 6: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

PyramidPyramid

► Base is any regular Base is any regular polygonpolygon

► All sides are All sides are trianglestriangles

Page 7: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

Platonic SolidsPlatonic Solids

►All sides are equalAll sides are equal►All angles are the sameAll angles are the same►All faces are identicalAll faces are identical►Same number of polygons meet at Same number of polygons meet at

each vertexeach vertex►Only five solids meet these criteria: Only five solids meet these criteria:

Platonic solidsPlatonic solids

Page 8: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

TetrahedronTetrahedron

► Composed of 4 Composed of 4 equilateral trianglesequilateral triangles

► 3 triangles meet at 3 triangles meet at vertexvertex

► Represented fire to Represented fire to the ancient Greeksthe ancient Greeks

Page 9: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

Hexahedron (Cube)Hexahedron (Cube)

► Composed of 6 Composed of 6 squaressquares

► 3 squares meet at a 3 squares meet at a vertexvertex

► Represented the Represented the stable earthstable earth

Page 10: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

OctahedronOctahedron

► Composed of 8 Composed of 8 equilateral trianglesequilateral triangles

► 4 triangles meet at 4 triangles meet at a vertexa vertex

► Represented airRepresented air

Page 11: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

DodecahedronDodecahedron

► Composed of 12 Composed of 12 equilateral equilateral pentagonspentagons

► 3 pentagons meet 3 pentagons meet at a vertexat a vertex

► Represented the 12 Represented the 12 signs of the Zodiacsigns of the Zodiac

Page 12: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

IcosahedronIcosahedron

► Composed of 20 Composed of 20 equilateral trianglesequilateral triangles

► 5 triangles meet at 5 triangles meet at a vertexa vertex

► Represented waterRepresented water

Page 13: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

Models of PolyhedraModels of Polyhedra

Page 14: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.
Page 15: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.
Page 16: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.
Page 17: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.
Page 18: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.
Page 19: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.
Page 20: Geometry: Part 2 3-D figures. Polyhedron ► 3-dimensional analog of a polygon ► Closed surface made up of polygons ► Any 2 polygons may have only one shared.

Unit 6 Introduction to Polygons This unit introduces Polygons. It defines polygons and regular polygons, and has the Polygon Angle Sum theorem. This unit.

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