Grade/Course: Geometry (Second Semester)
Instructional Unit 6: Similarity Transformations
Instructional Schedule: Third Nine Weeks (suggested for 20 days)
Adapted from Timothy Kanold Scope-and-Sequence documents
Standards:
(BA 2.4c.1) A dilation takes a line not
passing through the center of the
dilation to a parallel line, and leaves a
line passing through the center
unchanged.
Evidence Of Standard:
(student should be able to…)
Prerequisite Knowledge:
(standards linked to content taught in
previous grades)
Understand similarity in terms of similarity transformations. (key content)
-Explain the properties of dilations
given by a center and a scale factor.
-Perform dilations given by a center
and a scale factor on figures on a
plane.
-Verify that a dilation takes a line not
passing through the center of the
dilation to a parallel line, and leaves a
line passing through the center
unchanged.
(BA 2.4c.2) The dilation of a line
-Verify that the dilation of a line
segment is longer or shorter in the
segment is longer or shorter in the
ratio given by the scale factor.
ratio given by the scale factor.
(BA/PASS 2.4b) Given two figures, use -Explain similarity in terms of
the definition of similarity in terms of similarity transformations through
similarity transformations to decide if equality of all corresponding pairs of
they are similar; explain using
angles and the proportionality of all
similarity transformations the
corresponding pairs of sides.
meaning of similarity for triangles as
-Determine if two figures are similar,
the equality of all corresponding pairs including triangles.
of angles and the proportionality of all -Solve for missing side lengths of a
corresponding pairs of sides. Use
given figure using similarity ratios.
similarity ratios to solve for missing
side lengths.
(BA/PASS 2.4a) Use the properties of -Explain why, if two angle measures
similarity transformations to establish are known, the third angle is also
the AA criterion for two triangles to
known using the properties of
be similar.
similarity transformations.
Prove theorems involving similarity. (key content)
Assessment Tools:
(formative assessments, quizzes,
mastery tasks/activities)
(BA/PASS 2.4a) Prove theorems
about triangles which could use
postulates of similar triangles by AA,
SAS, and SSS. Theorems include: a
line parallel to one side of a triangle
divides the other two proportionally,
and conversely; the Pythagorean
Theorem proved using triangle
similarity.
-Prove theorems about triangles, such
as:
 A line parallel to one side of a
triangle divides the other two
proportionally, and
conversely
 Use triangle similarity to
prove the Pythagorean
Theorem
(BA/PASS 2.4b, 2.5b) Use congruence -Apply concepts of congruence and
and similarity criteria for triangles to
similarity criteria to:
solve problems and to prove
 Solve problems involving
relationships in geometric figures.
triangles
 Prove relationships in
geometric figures
Use coordinates to prove simple geometric theorems algebraically. (key content)
(BA/PASS 5.1) Find the point on a
directed line segment between two
given points (midpoint) that partitions
the segment in a given ratio.
-Recognize and understand the
standard formula for finding the
midpoint of a line segement.
-Find the coordinates for the midpoint
of a line segment.
Prove geometric theorems. (key content)
(BA/PASS 2.3b) Prove theorems
-Prove theorems about triangles such
about triangles. Theorems include:
as the segment joining midpoints of
measures of interior angles of a
two sides of a triangle is parallel to
0
the third side and half the length.
triangle sum to 180 ; base angles of
isosceles triangles are congruent; the
segment joining midpoints of two
sides of a triangle is parallel to the
third side and half the length; the
medians of a triangle meet at a point.
Note: Any italicized text denotes portions of a given standard that do not apply to identified standard content in this unit.
Resources/Exemplar Tasks:
( list possible task/activities students could engage in within this unit)
Standards for Mathematical Practice:
(highlight practice standards to be emphasized in the instructional unit)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of instruction.
8. Look for and express regularity in repeated reasoning.
( BA: Broken Arrow rigor standard; PASS: Priority Academic Student Skills standard; BA/PASS: Combination standard )