Unit 7 – Similarity and Transformations
Unit Objectives:
 to draw and interpret scale diagrams
 to apply properties of similar polygons
 to identify and describe line symmetry and rotational
symmetry
7.1 Scale Diagrams and Enlargements
Scale Diagram: A diagram that is an enlargement or reduction of
another diagram. Example:
Compare the corresponding (matching) sides of the diagrams.
The fraction
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑐𝑎𝑙𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑑𝑖𝑎𝑔𝑟𝑎𝑚
is called the scale factor of
the scale diagram.
If the corresponding sides have the same scale factor, the sides
are proportional.
Assignment: Page 322 – 324, #1 – 8, AFQ #11, Reflect
7.2 Scale Diagrams and Reductions
Investigate: page 325
A scale diagram can be smaller than the original diagram. This
type of scale diagram is called a reduction.
Assignment: Page 328 – 331, #1 – 11, 14, 20, AFQ #17, Reflect
7.3 Similar Polygons
When a polygon is an enlargement or reduction of another polygon,
the polygons are similar.
When two polygons are similar:
 corresponding sides are proportional
 corresponding angles are congruent (equal)
Assignment: Page 340 – 342, #1 – 7, 11, 13, AFQ #12, Reflect
7.4 Similar Triangles
When two polygons are similar: the measure of corresponding
angles must be equal AND the ratios of the lengths of
corresponding sides must be equal.
A triangle is a special polygon. Two triangles are similar when:
corresponding angles are equal OR corresponding sides are
proportional.
Are the following triangles similar?
Assignment: Pages 348 – 351, #1 – 7, 9 – 12, AFQ #8, Reflect
Mid-Unit Review: Page 352, # 1 – 7 all
7.5 Reflections and Line Symmetry
Investigate: Page 353
If you can reflect (or flip) a figure over a line and the figure
appears unchanged, then the figure has reflective symmetry or
line symmetry. The line that you reflect over is called the line of
symmetry. A line of symmetry divides a shape into two mirror
image halves.
Each point on one side of the line of symmetry has a
corresponding point on the other side. These points are the same
distance from the line of symmetry.
Assignment: Pages 357 – 359, #1 -6,8 – 10, AFQ #7, Reflect
7.6 Rotations and Rotational Symmetry
A shape has rotational symmetry when it coincides with itself
after a rotation of less that 360° about its center.
The number of times the shape coincides with itself during a
rotation of 360° is the order of rotation.
y
x
Assignment: Pages 365 – 367, #1 – 12, 14, 15,AFQ #13, Reflect
7.7 Identifying Types of Symmetry on the Cartesian Plane
Investigate: Page 368
When a shape and its transformation image are drawn, the
resulting diagram may show: no symmetry, line symmetry,
rotational symmetry or both line and rotational symmetry.
y
x
y
x
Assignment: Pages 373 – 375, #1 – 11, AFQ #12, Reflect
Unit Review: Page 377 – 379, # 1 – 19 all (hand –in assignment due
on the day of the test)
See Study Guide: Page 376
For Extra Practice – see Practice Test: Page 380
7.5 Reflections
Show video:
http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/4_Line_Symmetry/index.html
Here are some good websites/activities/videos for reflections/line symmetry:
Lessons/activities: http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=reflect
Interactive activity: http://www.mathsisfun.com/geometry/reflection.html
http://www.learner.org/courses/learningmath/geometry/session7/part_a/index.html
What is a tessellation? http://mathforum.org/sum95/suzanne/whattess.html
7.6 Rotations and Rotational Symmetry
Interactive - explore rotational symmetry of different designs/shapes:
http://www.learner.org/courses/learningmath/geometry/session7/part_b/i
ndex.html
interactive - explore the rotational symmetry of regular polygons:
http://www.analyzemath.com/Geometry/rotation_symmetry.html
tracing and rotating: http://www.subtangent.com/maths/ors.php