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Common Core Learning Standards
GRADE 8 Mathematics
GEOMETRY
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
8.G.1.
Verify experimentally the properties of
rotations, reflections, and translations:
8.G.1a.
Lines are taken to lines, and line segments to
line segments of the same length.
Concepts
Embedded Skills
Transformations Translate, rotate, and reflect lines and line
segments.
Explain the preservation of the sides of a figure
through a given transformation.
Identify corresponding parts between a figure and
its image using prime notation.
Show that lines are taken to lines and line
segments are taken to line segments.
Vocabulary
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Rotation
Reflection
Translation
Congruence
Transformation
Corresponding
parts
SAMPLE TASKS
I.)
On the given coordinate plane, graph and label the line segment who endpoints are A(1, 4) and B(5, 3).
̅̅̅̅ right 3 and down 4, label your image ̅̅̅̅̅̅
Translate 𝐴𝐵
𝐴′ 𝐵′ .
Name and explain what property is preserved under the translation.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
II.)
What type of transformation is being demonstrated?
̅̅̅̅ is taken to ̅̅̅̅̅̅
Under this transformation, 𝐻𝑇
𝐻′ 𝑇 ′ ,
compare the sizes of the two line segments.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
8.G.1.
Verify experimentally the properties of
rotations, reflections, and translations:
8.G.1b.
Angles are taken to angles of the same
measure.
Concepts
Embedded Skills
Transformations Translate, rotate, and reflect geometric shapes on
a coordinate plane.
Measure angles using a protractor.
Identify corresponding parts between a figure and
its image using prime notation.
Show that angles are taken to angles of the same
measure.
Vocabulary
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Rotation
Reflection
Translation
Congruence
Properties
Transformation
Corresponding
parts
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
SAMPLE TASKS
I.)
In the given transformation below, identify the
congruent angle pairs.
Using the given protractor, justify why your angles
pairs are congruent.
Given the following 90° clockwise rotation, label the
appropriate angles with A’, B’, and C’.
A
II.)

Explain why you chose the label for each angle.
B
C
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Embedded Skills
Transformations Translate, rotate, and reflect parallel lines on a
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
coordinate plane.
Explain that the slope and distance between two
parallel lines will be preserved after a translation,
rotation, or reflection of the parallel lines.
Identify corresponding lines after a translation,
rotation, or reflection, by using prime notation.
Show that parallel lines are translated, rotated, or
reflected parallel lines.
8.G.1.
Verify experimentally the properties of
rotations, reflections, and translations:
8.G.1c.
Parallel lines are taken to parallel lines.
Vocabulary
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Parallel lines
Rotation
Reflection
Translation
Transformation
Slope/rate of
change
Corresponding
parts
SAMPLE TASKS
I.
Translate parallel lines a and b, with the motion
rule (x +2, y – 1). Label the appropriate images
lines a’ and b’.
line a
line b
Find the slopes of your translated images. How do
the slopes of your transformations compare with
the slopes of the given parallel lines?
II.)
If two parallel lines are reflected over the y-axis, what characteristics of the original parallel lines are preserved after the
reflection? Sketch a diagram to help support your answer.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
Concepts
Congruent
figures
Embedded Skills
Explain the preservation of congruence when a
figure is rotated, reflected, and/or translated.
Describe the sequence of transformations that
occurred from the original 2D figure to the image.
8.G.2.
Understand that a two-dimensional figure is
congruent to another if the second can be
obtained from the first by a sequence of
rotations, reflections, and translations; given
two congruent figures, describe a sequence
that exhibits the congruence between them.
Vocabulary
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Transformation
Reflection
Rotation
Translation
Congruence
Corresponding
parts
sequence
SAMPLE TASKS
I.)

Figure B
What two transformations were used to get from
figure A to figure C?
Compare figure A with figure C, has any of the
characteristics of the figure changed after the two
transformations? Explain.
Figure A
Figure C
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
8.G.3.
Describe the effect of dilations, translations,
rotations, and reflections on two-dimensional
figures using coordinates.
Concepts
Embedded Skills
Transformations Dilate a two-dimensional figure using coordinates.
Describe the effect of dilating a two-dimensional
figure using coordinates.
Rotate a two-dimensional figure using coordinates.
Describe the effect of rotating a two-dimensional
figure using coordinates.
Translate a two-dimensional figure using
coordinates.
Describe the effect of translating a twodimensional figure using coordinates.
Reflect a two-dimensional figure using
coordinates.
Describe the effect of reflecting a two-dimensional
figure using coordinates.
Vocabulary
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Coordinate
Figure
Ordered pair
Reflect
Translate
Dilate
Rotate
Transformation
Prime
Image
X-axis
Y-axis
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
Concepts
Embedded Skills
Similarity with Explain the preservation of similarity when a figure
transformations is dilated, rotated, reflected, and/or translated.
Describe the sequence of transformations that
occurred from the original 2D figure to the image
to show the similarity.
8.G.4.
Understand that a two-dimensional figure is
similar to another if the second can be
obtained from the first by a sequence of
rotations, reflections, translations, and
dilations; given two similar two-dimensional
figures, describe a sequence that exhibits the
similarity between them.
Vocabulary
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Rotation
Reflection
Translation
Dilation
Transformation
Similarity
Congruent
Similar
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Embedded Skills
Understand congruence and
similarity using physical models,
transparencies, or geometry
software.
Prove/explain why the three angles of a triangle
equal 180°.
Prove/explain why the exterior angle theorem of a
triangle.
8.G.5.
Use informal arguments to establish facts
about the angle sum and exterior angle of
triangles, about the angles created when
parallel lines are cut by a transversal, and the
angle-angle criterion for similarity of triangles.
For example, arrange three copies of the same
triangle so that the sum of the three angles
appears to form a line, and give an argument
in terms of transversals why this is so.
Prove/explain why alternate interior angles are
congruent.
Prove/explain why alternate exterior angles are
congruent.
Prove/explain why corresponding angles are
congruent.
Prove/explain why angle-angle criterion works to
prove similarity of two triangles.
Vocabulary
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Triangle
Similar
Parallel lines
Transversal
Congruent
Supplementary
Linear pair
Corresponding
Vertical
Alternate,
exterior,
interior angles
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand and apply the
Pythagorean Theorem.
8.G.6.
Explain a proof of the Pythagorean Theorem
and its converse.
Concepts
Pythagorean
theorem
Embedded Skills
Explain a proof of Pythagorean theorem. (If a
triangle is a right triangle, then a2 + b2 = c2)
Explain a proof of the converse of Pythagorean
theorem. (If a2 + b2 = c2, then a triangle is a right
triangle)
Vocabulary
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Pythagorean
theorem
Converse
Proof
Legs
Hypotenuse
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand and apply the
Pythagorean Theorem.
8.G.7.
Apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in realworld and mathematical problems in two and
three dimensions.
Concepts
Embedded Skills
Pythagorean
theorem
Calculate the length of a leg of a right triangle using
Pythagorean theorem.
Calculate the length of the hypotenuse of a right
triangle using Pythagorean theorem.
Calculate the diagonal of a three-dimensional figure
using Pythagorean Theorem.
Read and interpret a word problem involving
Pythagorean Theorem.
Solve word problems involving Pythagorean
Theorem.
Vocabulary
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Leg
Hypotenuse
Right angle
Pythagorean
theorem
Square root
Radical
Diagonals
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Understand and apply the
Pythagorean Theorem.
8.G.8.
Apply the Pythagorean Theorem to find the
distance between two points in a coordinate
system.
Concepts
Pythagorean
theorem on a
coordinate
plane
Embedded Skills
Calculate the distance between two points in a
coordinate plane using the Pythagorean Theorem.
Vocabulary
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Leg
Hypotenuse
Right angle
Pythagorean
theorem
Ordered pair
Coordinate
plane
Square root
Distance
formula
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Solve real-world and mathematical
problems involving volume of
cylinders, cones, and spheres.
8.G.9.
Know the formulas for the volumes of cones,
cylinders, and spheres and use them to solve
real-world and mathematical problems.
Concepts
Embedded Skills
Write and solve using the formula for the volume
of a cone.
Write and solve using the formula for the volume of
a cylinder.
Write and solve using the formula for the volume of
a sphere.
Solve word problems involving the volume of cones,
cylinders, and spheres.
Vocabulary
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Volume
Cone
Cylinder
Sphere
Area
Base
Formula
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.