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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.

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Presentation on theme: "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."— Presentation transcript:

1 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

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

3 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.

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

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

6 Polyhedrons are classified by the number of faces. # faces 4 5 6 7 tetrahedron pentahedron hexahedron heptahedron

7 # faces 8 9 10 11 12 octahedron nonahedron decahedron undecahedron dodecahedron

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

9 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

10 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

11 #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

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

13 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

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

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


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