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

CCSS 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.

Then/Now 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 surfaces Face – 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 a three 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 Rectangles Cross Section:Vertically: Triangle Horizontally: Rectangle Angled: Triangle

Prism – Polyhedron with two parallel bases Name: Rectangular Prism Base: Two Rectangles Face: Rectangle Bases AND Four Rectangles Cross 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 Rectangles Cross 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 Rectangles Cross 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 Triangles Cross Section:Vertically: Triangle Horizontally: Rectangle Angled: Triangle, Quadrilateral

Pyramid – Polyhedron with one base and all other faces meet at a point Name: Pentagonal Pyramid Base: 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 Pyramid Base: 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: Octahedron Base: 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: Dodecahedron Base: 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: Icosahedron Base: NONE Faces: Twenty Equilateral Triangles Cross Section:Vertically: Hexagon Horizontally: Decagon Angled: Pentagon or Decagon

Example 3 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 #15-27, 40