LESSON 10.1 & 10.2 POLYHEDRONS OBJECTIVES: To define polyhedrons To recognize nets of space figures To apply Euler’s formula To describe cross section of 3-D figures

A POLYHEDRON is a solid figure formed by flat surfaces enclosed by polygons.

PARTS OF A POLYHEDRON FACES EDGES VERTEX the sides (flat surfaces) of a polyhedron the segment where two faces intersect. the point where three or more faces intersect.

Edge Face Vertex Rectangular prism How many faces does this polyhedron have? 6 Edges? Vertices? 12 8

Euler’s Formula :  Faces + Vertices = Edges + 2  OR F + V = E + 2

Polyhedrons are classified by the number of faces. # faces tetrahedron pentahedron hexahedron heptahedron

# faces octahedron nonahedron decahedron undecahedron dodecahedron

A net is a two-dimensional pattern that can be folded to form a three-dimensional figure.

Examples Using Nets #1 Identifying a net Is the given pattern a net for a cube? If so, name two letters that will be opposite faces. A B F C D E

Yes, the pattern is a net because it can be folded to form a cube. Opposite faces are: AC B E D F and A B F C D E

#2 Draw a net for the figure with a square base and four isosceles triangle faces. Label the net with its dimensions. 10 cm 8 cm 10 cm

#3 Use Euler’s Formula to find the number of vertices on a polyhedron with 8 triangular faces. F + V = E V = V = 14 V = 6 Calculate edges first. 8 faces * 3 sides = 24 24/2 = 12 edges (we do not want duplicate edges)

A cross section is the intersection of a solid and a plane. You can think of a cross section as a very thin slice of the solid. Lesson 10.2

What is the shape of each cross section? a. rectangle b. squarec. triangle d. circle e. square f. triangle

ASSIGNMENT Pg. 514 #1-9, 13-18, 20-21, 29a AND Pg. 524 #17-19, 40-42