GEOMETRY The dictionary is the only place where success comes before work. Mark Twain Today: Over...

GEOMETRY

The dictionary is the only place where success comes before work.

Mark Twain

Today: Over Vocab 12.1 Instruction Practice

12.1 Exploring Solids

Objectives: Know the properties of

polyhedrons Classify solids Identify Cross Sections

Vocabulary: on worksheet

Content Standards

G.GMD.4 Identify the shapes of two- dimensional cross-sections of three-dimensional objects, and identify three- dimensional objects generated by rotations of two-dimensional objects.

Mathematical Practices

5 Use appropriate tools strategically.

1 Make sense of problems and persevere in solving them.

You identified parallel planes and intersecting planes in three dimensional figures.

• Investigate cross sections of three- dimensional figures.

Polyhedron – a three dimensional figure bounded by flat surfacesFace – Each flat surfaceFace – Each flat surface

Edge: Meeting of two faces

Vertex: Point where three or more edges meet

Identify Cross Sections of Solids

Cross Section: Intersection of athree dimensional figure and a plane. : a “slice” of the figure

If the solid to the right is “cut”

by the plane it will form a triangle.

What would be formed if the solid was cut horizontally instead?

Solids Not Polyhedrons:

Name: Cylinder

Base: Two Circles

Faces: Two Circles

Cross Section:

Vertically: Rectangle

Horizontally: Circle

Angled: Ellipse or Parabola

Solids Not Polyhedrons:

Name: Cone

Base: One Circle

Faces: One Circle

Cross Section:

Vertically: Triangle

Horizontally: Circle

Angled: Parabola Or Ellipse

Solids Not Polyhedrons:

Name: Sphere

Base: NONE

Faces: NONE

Cross Section:

Vertically: Circle

Horizontally: Circle

Angled: Circle

Prism – Polyhedron with two parallel bases

Name: Triangular Prism

Base: Two Triangles

Faces: Triangle Bases AND Three RectanglesCross Section:

Vertically: Triangle

Horizontally: Rectangle

Angled: Triangle

Prism – Polyhedron with two parallel bases

Name: Rectangular Prism

Base: Two Rectangles

Face: Rectangle Bases AND Four RectanglesCross Section:

Vertically: Rectangle

Horizontally: Rectangle

Angled: Triangle, Rectangle, Pentagon and Hexagon

Prism – Polyhedron with two parallel bases

Name: Pentagonal Prism

Base: Two Pentagons

Faces: Pentagon Bases AND Five RectanglesCross Section:

Vertically: Pentagon

Horizontally: Rectangle

Angled: Triangle, Pentagon

Prism – Polyhedron with two parallel bases

Name: Hexagonal Prism

Base: Two Hexagons

Faces: Hexagon Bases AND Six RectanglesCross Section:

Vertically: Hexagon

Horizontally: Rectangle

Angled: Triangle, Rectangle, Hexagon

Pyramid – Polyhedron with one base and all other faces meet at a point

Name: Rectangular Pyramid

Base: One Rectangle

Faces: Rectangular Base and Four TrianglesCross Section:

Vertically: Triangle

Horizontally: Rectangle

Angled: Triangle, Quadrilateral

Pyramid – Polyhedron with one base and all other faces meet at a point

Name: Pentagonal PyramidBase: One Pentagon

Faces: Pentagonal Base AND Five Triangles

Cross Section:

Vertically: Triangle

Horizontally: Pentagon

Angled: Triangle, Pentagon

Pyramid – Polyhedron with one base and all other faces meet at a point

Name: Hexagonal PyramidBase: One Hexagon

Faces: Hexagonal Base AND Six Triangles

Cross Section:

Vertically: Triangle

Horizontally: Hexagon

Angled: Triangle, Quadrilateral, Hexagon

Platonic Solids: Regular Polyhedrons

: All faces regular and congruent

Name: Tetrahedron (Triangular Pyramid)Base: One Triangle

Faces: Four Equilateral Triangles

Cross Section:

Vertically: Triangle

Horizontally: Triangle

Angled: Triangle

Platonic Solids: Regular Polyhedrons

: All faces regular and congruent

Name: Hexahedron (Cube, Square Prism)Base: Two Squares

Faces: Six Squares

Cross Section:

Vertically: Square

Horizontally: Square

Angled: Triangle, Rectangle, Pentagon and Hexagon

Platonic Solids: Regular Polyhedrons

: All faces regular and congruent

Name: OctahedronBase: NONE

Faces: Eight Equilateral Triangles

Cross Section:

Vertically: Square

Horizontally: Square

Angled: Triangle, Quadrilateral, Hexagon

Platonic Solids: Regular Polyhedrons

: All faces regular and congruent

Name: DodecahedronBase: NONE

Faces: Twelve Regular Pentagons

Cross Section:

Vertically: Decagon

Horizontally: Decagon

Angled: Triangle, Square or Hexagon

Platonic Solids: Regular Polyhedrons

: All faces regular and congruent

Name: IcosahedronBase: NONE

Faces: Twenty Equilateral Triangles

Cross Section:

Vertically: Hexagon

Horizontally: Decagon

Angled: Pentagon or Decagon

A. Cut the cone parallel to the base.

B. Cut the cone perpendicular to the base through the vertex of the cone.

C. Cut the cone perpendicular to the base, but not through the vertex.

D. Cut the cone at an angle to the base.

A solid cone is going to be sliced so that the resulting flat portion can be dipped in paint and used to make prints of different shapes. How should the cone be sliced to make prints in the shape of a triangle?

Net and Surface Area:

Net: “Unfolding” of three dimensional shape.

Surface Area: Sum of the areas of all the faces.

25 cm

15 cm

Draw a net for the pentagonal prism to find the surface area.

GEOMETRY

The dictionary is the only place where success comes before work.

Mark Twain

Assignment: Section 12.1 p. 842

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