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Partners for Student Success
Grade 8 Geometry Semester
Unit 1: Geometric Measurement & Dimensions
In order for your child to be successful, it is important to be consistent with the mathematical
vocabulary and processes that will be implemented this year in geometry. You may find this
resource helpful when supporting your child at home.
Unit Concepts
Concept
Explanation
Dissection
Argument
When trying to determine
the volume of an
unknown solid, you can
cut the solid into pieces,
and rearrange the pieces
into a solid with a known
formula for volume.
Cavalieri’s
Principle
If two solids have the
same height and the same
cross-sectional area at
every level, then they
have the same volume.
Examples
Example:
Informal
Argument
An argument based on the
premise that what is
obvious is true.
Volume
The number of cubic units
contained in the interior
of a solid.
Three
Dimensional
Any solid with length,
width, and height.
Cecil County Public Schools
2014 – 2015
Real World Examples: How much soil is needed to fill a
rectangular flower box? How much water fits in a 4-foot
pool shaped as a cylinder?
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Grade 8 Geometry Semester
Unit 1 Partners for Student Success
Concept
Explanation
Cross Section
The intersection of a
plane and a solid.
Cylinder
A solid with congruent
circular bases that lie in
parallel planes.
Pyramid
A solid with a polygon
base and lateral faces
which are triangles that
share a common vertex.
Cone
A solid that has a circular
base and a vertex that is
not in the same plane as
the base.
Sphere
The set of all points in
space equidistant from a
given point called the
center.
Cecil County Public Schools
2014 – 2015
Examples
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Grade 8 Geometry Semester
Unit 1 Partners for Student Success
Concept
Explanation
Midpoint
A point that divides, or
bisects, a segment into
two congruent segments.
Distance
Formula
A form of the
Pythagorean Theorem
Partition
Segment
Formula
A formula used to find a
point on a line that
divides the line into a
given ratio.
Perpendicular
lines
Lines or line segments
that intersect and form a
90° angle (a right angle)
Parallel Lines
Lines or line segments in
the same plane that do not
intersect. Parallel lines
have the same slope
Vertical Angles
Angles across from each
other when two lines or
segments intersect.
Vertical angles are
congruent.
Perpendicular
Lines
Two lines that intersect to
form a right angle.
Corresponding
Angles
Two angles that are
formed by two lines and
a transversal and
occupy corresponding
positions.
Cecil County Public Schools
2014 – 2015
Examples
k x k x k y k y 
P( x, y )   2 1 1 2 , 2 1 1 2 
k1  k 2 
 k1  k 2
In the diagram, angles 1 and 3 are vertical angles; angles 2
and 4 are vertical angles
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Grade 8 Geometry Semester
Unit 1 Partners for Student Success
Concept
Explanation
Linear Pair
Two adjacent angles
whose noncommon
sides are opposite rays.
Examples
In a right triangle, the
square of the length of
Pythagorean
the hypotenuse is equal
Theorem
to the sum of the
squares of the lengths
of the legs.
A type of proof written
as numbered statements
Two-Column
and corresponding
Proof
reasons that show an
argument in a logical
order.
Additional Resources
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www.corestandards.org
o View the math standards your child will be learning this year. Scroll down and click
“Mathematics Standards” to download the pdf document.
www.ixl.com/math/standards/common-core
o Click “High School” to find interactive practice opportunities aligned with each math
standard.
www.studyjams.com
o Using the search bar, find interactive examples and opportunities for practice for any
given concept.
www.khanacademy.org
o Using the search bar, find videos and examples on several math concepts throughout
the year
http://www.shmoop.com/common-core-standards
o Using the anchor standard, subtopic, and standard to unpack each standard.
Cecil County Public Schools
2014 – 2015
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Grade 8 Geometry Semester
Unit 1 Partners for Student Success