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CCSS.Math.Content.7.G.A.3
3Describe the two-dimensional figures thatresult from slicing three-dimensional figures, as
in plane sections ofright rectangular prismsand right rectangularpyramids.
http://www.corestandards.org/Math/Content/7/G/A/3http://www.corestandards.org/Math/Content/7/G/A/3http://www.corestandards.org/Math/Content/7/G/A/37/29/2019 7th Geometry Standard 3
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Faces,Vertices, and
Edges
http://cdn.virtuallearningcourses.com/ivtcontent/images/11-1%20Space%20Figures
http://cdn.virtuallearningcourses.com/ivtcontent/images/11-1%20Space%20Figures%20and%20Cross%20Sections.pdfhttp://cdn.virtuallearningcourses.com/ivtcontent/images/11-1%20Space%20Figures%20and%20Cross%20Sections.pdfhttp://cdn.virtuallearningcourses.com/ivtcontent/images/11-1%20Space%20Figures%20and%20Cross%20Sections.pdfhttp://cdn.virtuallearningcourses.com/ivtcontent/images/11-1%20Space%20Figures%20and%20Cross%20Sections.pdfhttp://cdn.virtuallearningcourses.com/ivtcontent/images/11-1%20Space%20Figures%20and%20Cross%20Sections.pdfhttp://cdn.virtuallearningcourses.com/ivtcontent/images/11-1%20Space%20Figures%20and%20Cross%20Sections.pdf7/29/2019 7th Geometry Standard 3
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Faces
Edge
Vertices
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Problem 1
Identifying Vertices, Edges, and Faces
How many vertices, edges, and faces are in the polyhedron at
the right? List them.
ere are ve vertices: D, E, F, G, and H.
ere are eight edges: DE, EF, FG, GD, DH, EH, FH, and GH.
ere are ve faces: nDEH, nEFH, nFGH, nGDH, and quadrilateral DEFG.
H
D
G
t
H
F
ED
G
?
How many Vertices? Name them.
How many Edges? Name them.
How many Faces? Name them.
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Faces, Vertices,and Edges
Activity
Print the next 2 slides on one page
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H
F
ED
G
How many Vertices? Name them.
How many Edges? Name them.
How many Faces? Name them.
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R
S
U V
T
W
How many Vertices? Name them.
How many Edges? Name them.
How many Faces? Name them.
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Problem 2
Using Eulers Formula
How many vertices, edges, and faces does the polyhedron at the right
have? Use your results to verify Eulers Formula.
Count the number offaces.
Count the number ofvertices.
Count the number ofedges.
Substitute the values intoEulers Formula.
F 5 8
V 5 1 2
E 5 1 8
F 1 V 5 E 1 2
81
1 20
1 81
220 5 20
Key Concept Eulers Formula
e sum of the number of faces (F) and vertices (V) of a polyhedron is two more than the
number of its edges (E).
F1 V5 E1 2
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Problem 4
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.
Describing a Cross Section
What is the cross section formed by the plane and the solid
at the right?
e cross section is a rectangle.
This cross sectionis a triangle.
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Problem 5
Drawing a Cross Section
Visualization Draw a cross section formed by a vertical plane
intersecting the front and right faces of the cube. What shape
is the cross section?
Step 1
Visualize a vertical plane intersecting
the vertical faces in parallel segments.
Step 2
Draw the parallel
segments.
Step 3
Join their endpoints.
Shade the cross section.
e cross section is a rectangle.
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8.
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Extension:
Writing Cross sections are used in medical training and research. Research and
write a paragraph on how magnetic resonance imaging (MRI) is used to study crosssections of the brain.
Writing Assignment
An MRI is similar to a computerized topography (CT) scanner in that it produces cross-sectional
images of the body. Looking at images of the body in cross section can becompared to looking at the inside of a loaf of bread by slicing it.Unlike a CT scan, MRI does not use X-rays. Instead, it uses a strong magnetic field and radio wavesto produce very clear and detailed computerized images of the inside of the body. MRI is commonlyused to examine the brain, spine, joints, abdomen, and pelvis. A special kind of MRI exam, calledmagnetic resonance angiography (MRA), examines the blood vessels.
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