7th geometry standard 3

7/29/2019 7th Geometry Standard 3

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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/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.pdf


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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





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R

S

U V

T

W





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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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7th geometry standard 3

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