8
th
Grade
Mathematics
Unit 1:
Transformations,
Congruency, and
Similarity
Excerpts from Georgia Department of
Education Webinar May 1, 2012
melissa.stewart@hallco.org
May 2012
Warm-Up
Are the following two figures congruent? Use
transformations to justify your answer.
Teaching videos can be found at
http://secc.sedl.org/common_core_videos/index.php?action=view&id=78
1
melissa.stewart@hallco.org
May 2012
What’s the main idea of Unit 1?
• Developing deep understanding of
transformations of geometric figures.
• Using informal arguments to
establish geometric facts.
melissa.stewart@hallco.org
May 2012
Concepts & Skills to Maintain from Previous Grades
 Number sense
 Computation whole numbers and decimals, including
order of operations
 Addition and subtraction of common fractions with
like denominators
 Measuring length and finding perimeter and area of
rectangles and squares
 Characteristics of 2-D and 3-D shapes
 Data usage and representation
Websites to help with the above:
www.aaamath.com
http://www.arcademicskillbuilders.com/
http://www.professorgarfield.org/pgf_home.html
http://multiplication.com/
melissa.stewart@hallco.org
May 2012
Enduring Understandings from this Unit
 Coordinate geometry can be a useful tool for
understanding geometric shapes and transformations
 Reflections, translations, and rotations are actions that
produce congruent geometric objects
 A dilation is a transformation that changes the size of a
figure, but not the shape
 The notation used to describe dilation includes a scale
factor and a center of dilation.
 If the scale factor of a dilation is great than 1, the
image resulting from the dilation is an enlargement. If
the scale factor is less than 1, the image is a reduction.
 Two shapes are similar if the lengths of all the
corresponding sides are proportional AND all the
corresponding angles are congruent.
 Two similar figures are related by a scale factor, which
is the ratio of the lengths of the corresponding sides.
 Congruent figures have the same size and shape. If
the scale factor of dilation is equal to one, the image
resulting from the dilation is congruent to the original
figure.
 When parallel lines are cut by a transversal,
corresponding, alternate interior and alternate exterior
angles are congruent.
melissa.stewart@hallco.org
May 2012
Examples & Explanations
1.
melissa.stewart@hallco.org
May 2012
2. Use informal arguments to establish facts about:
 the angle sum and exterior angle of triangles.
 the angles created when parallel lines are cut by
a transversal.
 the angle-angle criterion for similarity of
triangles.
melissa.stewart@hallco.org
May 2012
melissa.stewart@hallco.org
May 2012
3. Understand congruence and similarity using
physical models, transparencies, or geometry
software.
melissa.stewart@hallco.org
May 2012
melissa.stewart@hallco.org
May 2012
For more practice
http://secc.sedl.org/common_core_videos/index.p
hp?action=view&id=781
melissa.stewart@hallco.org
May 2012
 The student edition for Unit 1 can be
found at
https://www.georgiastandards.org/C
ommon-Core/Pages/Math-6-8.aspx
On the left side, please look under
mathematics, 6 – 8. Then, the right
side has a pull-down menu to access
the units.
 Additional parent guides will be
posted to the parent resource page on
http://www.hallco.org/boe/index.ph
p (right had menu) as they become
available.
melissa.stewart@hallco.org
May 2012