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
#15-27, 40