1 geometry section 6-1c exploring polyhedrons pg. 409 quiz tomorrow
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Geometry Section 6-1C Geometry Section 6-1C
Exploring PolyhedronsExploring Polyhedrons
Pg. 409Pg. 409
Quiz TomorrowQuiz Tomorrow
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Pg.410
Definitions:Definitions:
Polyhedron: Three-dimensional figures whose faces are triangles, rectangles and other polygons.
Remember – “names” have letters ABCDE, “classifications” are the
specific names of the shape.
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The polyhedron shown is a cube with a corner cut off.
a. Name the triangular face of the polyhedron.
b. Name the face that includes L, M and Q as vertices.Pg.410
Try It:Try It:
c. Find the number of faces, vertices and edges of the polyhedron.
RST
MLQRT
Faces - 7 Vertices - 10 Edges - 15
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Pg.410
Polygons (2-D) are classified by the number of sides they have.
Polyhedrons (3-D) are classified by the number of faces they have.
4 faces – tetrahedron 5 faces – pentahedron6 faces – hexahedron 8 faces – octahedron12 faces – dodecahedron 20 faces - icosahedron
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Pg.411
ExploreExplore
# of faces (F)
# of vertices (V)
# of edges (E)
a.
b.
c.
d.
e.
Find the number of faces, vertices and
edges in each polyhedron.
Can you see the relationship between
these numbers?
46875
486
106
61212159
Euler’s Formula
F + V – E = 2 or F + V = E + 2
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1. Name the faces of the polyhedron.
#1-4
Pg.412
Exercises:Exercises:
DEF, ABEF, BCDE, ACDF, ABC
2. Classify the polyhedron
pentahedron
3. Find the number of faces, vertices and edges.
F - 5 V - 6 E - 9
4. Verify Euler’s Formula
5 + 6 – 9 = 2
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5. Classify faces 1 and 2
#5-8
Pg.412
Exercises:Exercises:
1 - triangle
6. Name the vertices of face 1.
P, Q, V
7. Name the sides of face 2.
NP, PQ, QR, RS, ST, TU, UM, MN
8. How many faces, vertices and edges? Verify Euler’s Formula
F - 14
2 - octagon
V - 24 E - 36 14 + 24 – 36 = 2
14 + 24 + 2 = 36
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Homework: Practice 6-1CQuiz Tomorrow