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Course: Math 8
Unit: Congruence and Similarity
Unit Length: 8 Lessons
Overview:
In this unit you will investigate the effect of transformations on two-dimensional figures. You will then use
transformations to explore relationships between angles formed when parallel lines are cut by a transversal and among
angles in a triangle. Throughout the unit, you will perform translations, reflections, rotations, and dilations and learn
about congruency and similarity. You will deepen your knowledge of geometry and see connections between geometry
and algebra.
Next Generation Content Standards and Objectives:
M.8.G.1
verify experimentally the properties of rotations, reflections and translations:
a. lines are taken to lines, and line segments to line segments of the same length.
b. angles are taken to angles of the same measure.
c. parallel lines are taken to parallel lines. (CCSS Math.8.G.1)
M.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. (CCSS Math.8.G.2)
M.8.G.3
describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
(CCSS Math.8.G.3)
M.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. (CCSS Math.8.G.4)
M.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. (CCSS Math.8.G.5)
WVU K12 Partnerships Unit Overview Construction Tool
Standards for Mathematical Practices:
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Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Driving question:
What effect do translations, reflections, rotations, and dilations have on two-dimensional figures and how does
this apply to relationships among angles created when parallel lines are cut by a transversal and among the
angles in a triangle?
Overview script:
The topics you will study in this Geometry unit are used in a variety of professions.
For example, these skills are found throughout the construction industry. Draftsmen create blueprints of
buildings and other structures. In mathematics, these diagrams can be called dilations of the actual structure.
As the diagrams are turned into products, architects, engineers, and contractors apply their understanding of
similar figures.
Transformations are also often found in the materials used in homes or other buildings. Tile, brick, stone, and
wood are often arranged in patterns using transformations, often requiring an understanding of the angles of a
triangle. Because they are so rigid, triangles are the foundation of architecture and engineering.
Other careers that rely on these skills can be closely related to interior design, graphic design, advertising, and
computer graphics.
Throughout this unit, you will experiment with geometric transformations to develop ideas that you think are true
about them.
You will learn what it means for figures to be congruent and, using a sequence of these transformations translations, reflections, and rotations - you will show that two figures are congruent. You will see connections
with algebra by investigating transformations in the coordinate plane.
You will also learn what it means for figures to be similar and using a sequence of transformations that now
include dilations, you will show that the two figures are similar.
You will use your understanding of congruence and similarity to describe and analyze two-dimensional figures.
Investigations will allow you to deepen your knowledge about parallel lines and triangles.
WVU K12 Partnerships Unit Overview Construction Tool
The students will know:
Geometric terminology
Properties of translations, reflections, rotations, and dilations
Properties of congruent figures
Properties of similar figures
Sum of angles of a triangle
Relationship between interior and exterior angles of a triangle
Relationship of angles created by parallel lines cut by a transversal
Angle-angle criteria for similarity of triangles
The students will do:
Translate figures
Reflect figures
Rotate figures
Apply theorems and postulates to determine angle measures of triangles
Apply theorems and postulates in real-world situations
Select appropriate tools strategically in investigations and tasks
Progress from intuitive inducing of conclusions to formal deductions