Solid Geometry Student Expectations 7 th Grade 7
- Slides: 14
Solid Geometry
Student Expectations 7 th Grade: 7. 3. 6 C Use properties to classify threedimensional figures, including pyramids, cones, prisms, and cylinders.
Three Dimensions Solid Geometry is the geometry of three-dimensional space It is called threedimensional, or 3 D because there are three dimensions: width, depth and height.
Three-dimensional figures have faces, edges, and vertices. A face - is a flat surface, and edge - is where two faces meet, and a vertex - is where three or more edges meet.
In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges of a cube.
Polyhedron A geometric object with flat faces and straight edges. a polyhedron is a three - dimensional figure made up of sides called faces, each face being a polygon.
Base The lowest part. The surface that a solid object stands on, or the bottom line of a shape such as a triangle or rectangle.
Prism A solid object that has two identical ends and all flat sides. The cross section is the same all along its length. The shape of the ends give the prism a name, such as "triangular prism“ It is a polyhedron.
Pyramid A solid object where: * The base is a polygon (a straight-sided shape) * The sides are triangles which meet at the top (the apex). It is a polyhedron.
Cylinder A cylinder is a solid object with: * two identical flat circular or elliptical ends * and one curved side.
Cone A solid (3 -dimensional) object that has a circular base and one vertex
Prisms & Pyramids Type Triangular Prism Rectangular Prism Cube Square Pyramid Triangular Pyramid Examples Properties ● 5 faces 2 triangular bases 3 rectangular faces ● 9 edges ● 6 vertices 6 faces 2 rectangular bases 4 rectangular faces ● 12 edges ● 8 vertices ● 6 faces 2 square bases 4 square faces ● 12 edges ● 8 vertices ● 5 faces 1 square base 4 triangular faces ● 8 edges ● 5 vertices ● 4 faces 1 triangular base 3 triangular faces ● 6 edges ● 4 vertices
Three Dimensional Figures with Curved Surfaces Type Example Properties ● 2 circular bases Cylinder ● 1 curved surface Cone ● 1 curved surface ● 1 circular base ● 1 vertex Sphere ● 1 curved surface
Drawing a 3 D Figure 3 -dimensional objects can also be depicted as 2 -dimensional drawings taken at different views. These representations are called orthogonal drawings. The 3 -dimensional drawing at the left is represented by the 2 -dimensional drawings from the top, front and right-side views.
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