1. Space Figures & Cross-Sections

2. Vocab Polyhedron - 3-dimensional figure whose surfaces are polygons
Face of polyhedron - each polygon that forms the polyhedron
Edge - segment formed by the intersection of two faces
Vertex - point where 3 or more edges intersect
Cross-section – the intersection of a solid & a plane.

3. Vocab Ctd.

4. Euler’s Formula

5. Group Activity
Each group will construct several 3-dimensional figures from nets
Groups will then record data and make conjectures on the relationship between faces, edges and vertices of a polyhedron

6. Use Euler’s Formula to find the number of edges on a solid with 6 faces and 8 vertices.
F + V = E + 2 Euler’s Formula
6 + 8 = E + 2 Substitute the number of faces and vertices.
12 = E Simplify.
A solid with 6 faces and 8 vertices has 12 edges.

7. You try
Use Euler’s formula to find the number of edges on a polyhedron with eight triangular faces.
12 edges

8. Cross Sections Describe this cross section.
The plane is parallel to the triangular base of the figure, so the cross section is also a triangle.

9. You try
Describe the cross-section.

10. Drawing Cross Sections
Draw and describe a cross section formed by a vertical plane intersecting the top and bottom faces of a cube.
If the vertical plane is parallel to opposite faces, the cross section is a square.
Sample: If the vertical plane is not parallel to opposite faces, the cross section is a rectangle.

11. You try
Draw & describe the cross section formed by a horizontal plane intersecting the left and right faces of the cube.

12. Closure