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Partners for Student Success
Geometry
Unit 2: Stability and Change: Constructions, Congruence,
and Transformations
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
Examples
Constructions
Using a compass,
straightedge, computer
software, patty paper, or
other devices to explore
and/or justify properties
Regular Polygon
A two-dimensional figure
with straight edged sides
where all sides are
congruent (equilateral)
and all angles are
congruent (equiangular)
Transformations
Manipulating a figure by
translations, rotations,
reflections, and/or
dilations
Translation – sliding a figure
Rotation – turning a figure
Reflection – making a mirror image
Dilation – enlarging or reducing a figure
Rigid Motion
A figure undergoes a
series of transformations
and remains congruent to
the original figure.
A series of translations, rotations, and/or reflections
preserve congruence. Dilations are an example of non-rigid
motion.
Quadrilateral
A four-sided polygon
Squares, rectangles, trapezoids, parallelograms, kites, and
rhombuses are all examples of quadrilaterals
Same size and same shape
Congruent
Congruent polygons have
angles that are the same
measure, shapes that are
the same, and side lengths
that are equal
Cecil County Public Schools
2014-2015
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Common Core Geometry
Unit 2 Partners for Student Success
Concept
Explanation
Trapezoid
A quadrilateral (4-sided
polygon) with one pair of
parallel sides
Pre-image
A figure or polygon
before a transformation or
series of transformations
was performed (the
original figure)
Image
A figure or polygon after
a transformation or series
of transformations was
performed
Rigid Motion
A figure undergoes a
series of transformations
and remains congruent to
the original figure.
Triangle
Congruence
Techniques to justify that
triangles are congruent,
including ASA, SAS,
SSS, and AAS
Deductive
Reasoning
Student use facts,
definitions, theorems, and
properties to justify
conclusions
Median of a
Triangle
A line segment in a
triangle from the vertex of
a triangle to the midpoint
of the opposite side.
Triangles have 3 medians.
Proof
Students will justify why
an answer is correct or
why a property is true
Cecil County Public Schools
2014-2015
Examples
A series of translations, rotations, and/or reflections
preserve congruence. Dilations are an example of non-rigid
motion.
Medians intersect at the same point called the centroid.
Students may use the traditional 2-column proof, or they
may use other techniques, such as a paragraph, flow chart,
or graphic. Proper terminology must be used in the
justification
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Common Core Geometry
Unit 2 Partners for Student Success
Concept
Explanation
Inscribed
Another shape is inside
another shape, but still
touching
Circumscribed
A shape is outside another
shape, but still touching
the other shape
Diagonals of a
Quadrilateral
Diagonals connect nonadjacent vertices.
Examples
In the shape above on the left, the circle is
circumscribed; the hexagon is inscribed. But in the
shape on the right, the triangle is not inscribed because
the vertices are not on the circle
Segment BD is one of the diagonals of parallelogram
ABCD.
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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Common Core Geometry
Unit 2 Partners for Student Success