Download Name: :_____ Unit 4: Similarity Through Transformations

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Unit 3: Properties of Triangles
Big Idea: Triangles always have specific properties regarding their angles and side lengths.
Essential Questions
 What are the relationships between sides and interior angles of a triangle?
 What are the restrictions on the side lengths of a triangle?
 What is the relationship between the sides of 45-45-90 triangles and 30-60-90 triangles?
Learning Target
A
B
C
D
E
F
Text
I can use and prove the Triangle Sum Theorem.
3.1
I understand and can explain the relationship between interior angle measures and
their opposing sides.
I can use and prove the Exterior Angle Theorem, and the Exterior Angle Inequality
Theorem.
I can use and prove the Triangle Inequality Theorem. (i.e. range of potential third
side)
I can use the Pythagorean Theorem.
3.1,
3.2
I can use special triangle ratios to find missing sides and identify angles for 45-4590 and 30-60-90 triangles.
I know
it
I partially
get it
I don’t
get it
3.1
3.2
3.3
3.3,
3.4
Unit 4: Similarity Through Transformations
Big Idea: Triangles can be similar
Essential Questions
How do I use and set up proportions to solve real world problems (ratios, shadows, similar triangles, etc.).
How do I determine whether two triangles are similar?
What is the geometric mean useful for?
Learning Target
A I can identify the conditions necessary to prove if two triangles are similar.
I can determine and use the scale factor of a dilation to calculate similar geometry using
B
proportions.
C I can use constructions to explore AA, SAS, and SSS similarity theorems.
I can use and prove the Angle-Bisector Theorem, Triangle Proportionality Theorem, Converse
D of the Triangle Proportionality Theorem, Proportional Segments Theorem, and Triangle
Midsegments Theorem.
I understand and can explain the similar triangles created when drawing the altitude from the
E
hypotenuse of a right triangle (Right Triangle Altitudes Similarity Theorem).
F I can use the geometric mean to solve for the unknown lengths of a right triangle.
I can prove the Pythagorean Theorem and the Converse of the Pythagorean Theorem.
G
(assessed via group project)
I can use similar triangles and proportions as they apply to real world problems (i.e. height of
H
building, height of tree)
Text
4.1
4.1
4.2
4.3
4.4
4.4
4.5
4.6
I know
it
I partially
get it
I don’t get
it
Assignment
Date
Quiz #
Score
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