1. 10-1: Introduction to Solids
Grade Distribution
1st
2nd
6th
7th A 4 5 6 B 11 C 2 3 D F 7 9 8
No Show(s) 1
Range
51-95
55-99
59-97
40-96
Mean
77.17
78.90
78.11
75.93
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10-1: Introduction to Solids

2. Introduction to Solids
Section 10–1
Geometry PreAP, Revised ©2014
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10-1: Introduction to Solids

3. 10-1: Introduction to Solids
Definitions
Three-dimensional figures, or solids, can be made up of flat or curved surfaces, with a length, width, and height.
Face is a flat surface.
Edge is the segment that is the intersection of two faces.
Vertex is the point that is the intersection of three or more faces.
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10-1: Introduction to Solids

4. 10-1: Introduction to Solids
Parts of a Polyhedron
A solid formed by polygons that enclose a single region of space is called a polyhedron.
Polygonal region = face
Intersection of 2 faces = edge
Intersection of 3+ edges = vertex
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10-1: Introduction to Solids

5. 10-1: Introduction to Solids
Definitions
Cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.
Prism is formed by two parallel congruent bases and connected by faces
Cylinder is formed by two parallel congruent to circular bases and curved bases
Pyramid is formed by a polygonal base and triangle bases that meet at a vertex
Cone is formed by having a circular base and a curved surface connected to a vertex
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10-1: Introduction to Solids

6. 10-1: Introduction to Solids
Bases
Prisms and pyramids are named according to the shape of the base.
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10-1: Introduction to Solids

7. 10-1: Introduction to Solids
Example 1
Name the vertices, edges, and bases of this cube.
vertices: A, B, C, D, E, F, G, H
edges:
bases: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF
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10-1: Introduction to Solids

8. 10-1: Introduction to Solids
Your Turn
Classify the figure. Name the vertices, edges, and bases of this shape.
cone
vertex: N
edges: none
base: •M
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10-1: Introduction to Solids

9. 10-1: Introduction to Solids
Nets
Imagine cutting a 3-D solid along its edges and laying flat all of its surfaces. This 2-D figure is a net for that 3-D solid.
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10-1: Introduction to Solids

10. 10-1: Introduction to Solids
Example 2
Describe the three-dimensional figure that can be made from the given net. Determine the shape and how many congruent square faces it has.
The net has six congruent square faces. So the net forms a cube.
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10-1: Introduction to Solids

11. 10-1: Introduction to Solids
Example 3
Describe the three-dimensional figure that can be made from the given net. Determine the shape and how many congruent faces it has.
The net has one circular face and one semicircular face. These are the base and sloping face of a cone. So the net forms a cone.
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10-1: Introduction to Solids

12. 10-1: Introduction to Solids
Your Turn
Describe the three-dimensional figure that can be made from the given net. Determine the shape and how many congruent faces it has.
The net has four congruent triangular faces. So the net forms a triangular pyramid.
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10-1: Introduction to Solids

13. 10-1: Introduction to Solids
Cross Sections
A cross section is the intersection of a three-dimensional figure and a plane.
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10-1: Introduction to Solids

14. 10-1: Introduction to Solids
Example 4
Describe the cross section. What type of shape does it make?
Pentagon
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10-1: Introduction to Solids

15. 10-1: Introduction to Solids
Your Turn
Describe the cross section. What type of shape does it make?
Point
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10-1: Introduction to Solids

16. 10-1: Introduction to Solids
Assignment
Page all, all, 41, 42
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10-1: Introduction to Solids