Download Unit Title: Suggested Time

CMS Curriculum Guides 2011-2012
Course Title Geometry
Unit 5:
Similarity, Right Triangles and Trigonometry
Suggested Time: 16 days
Enduring understanding (Big Idea): Similarity, Reasoning & Proof, Visualization, Measurement, Coordinate Geometry
Essential Questions:
(1)
(2)
(3)
(4)
How do you use proportions to find side lengths in similar polygons?
How do you prove that two triangles are similar?
How do you identify corresponding parts in similar triangles?
If you know the measures of 2 sides or a side and an angle of a right
triangle, how can you use them to find the remaining sides and angles?
(5) How can you use angles of depression or elevation to solve real world
problems?
(6) How can you solve non-right triangles?
Common Core Standards
G-SRT.2 Given two figures, use
the definition of similarity in terms
of similarity transformations to
decide if they are similar; explain
using similarity transformations the
meaning of similarity for triangles as
the equality of all corresponding
pairs of angles and the
proportionality of all corresponding
pairs of sides.
Textbook Alignment
7-2 Similar Polygons
Supplement: Prove that all
circles are similar
Mathematical Practices
(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 structure.
(8) Look for and express regularity in repeated reasoning.
Connection to 2003
Standards
Additional Notes
2.03 Apply properties,
definitions, and theorems of
two-dimensional figures to
solve problems and write
proofs. (c) polygons
Foundations of Geometry
Emphasize vocabulary
2.03 Apply properties,
definitions, and theorems of
Foundations of Geometry: Informal
proofs of theorems are appropriate.
G.C.1 Prove that all circles are similar.
G-SRT.3 Use the properties of
similarity transformations to
establish the AA criterion for two
1
7-3 Proving Triangles are Similar
CMS Curriculum Guides 2011-2012
Course Title Geometry
triangles to be similar.
two-dimensional figures to
solve problems and write
proofs. (a) triangles
G-SRT.4 Prove theorems about
triangles.
G-SRT.5 Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
G-SRT.4 Prove theorems about
triangles. Example: The altitude to
the hypotenuse of a right triangle
divides the triangle into 2 triangles
that are similar to the original
triangle and to each other.
7-4 Similarity in Right Triangles
Regular: Try a patty paper proof of
the theorem at the left.
G-SRT.5 Use congruence and
similarity criteria for triangles to
solve problems and to prove
relationships in geometric figures.
Honors: Students should be able to
develop the proof of the theorem
themselves.
G-SRT.4 Prove theorems about
triangles. Theorems include: a line
parallel to one side of a triangle
divides the other two proportionally,
and conversely.
7-5 Proportions in Triangles
G.CO.4 Prove theorems involving
similarity. Prove the Pythagorean
Theorem using triangle similarity.
8-1 Pythagorean Theorem and Its
Converse
8-2 Special Right Triangles (4545-90 and 30-60-90)
2
Foundations of Geometry should
concentrate on making connections
between theorems and setting up and
solving equations to determine
measures.
Foundations of Geometry should
concentrate on making connections
between theorems and setting up and
solving equations to determine
measures.
CMS Curriculum Guides 2011-2012
Course Title Geometry
G.SRT.6 Understand that by
similarity, side ratios in right
triangles are properties of the angles
in the triangle, leading to definitions
of trigonometric ratios for acute
angles.
8-3 Trigonometry
8-4 Angles of Elevation and
Depression
1.01 Use trigonometric ratios
to model and solve problems
in right triangles.
Suggestion: Split the unit at this
point.
G.SRT.7 Explain and use the
relationship between the sine and
cosine of complementary angles.
G.SRT.8 Use trigonometric ratios
and the Pythagorean Theorem to
solve right triangles in applied
problems.*
G.SRT.10 (+) Prove the Laws of
Sines and Cosines and use them to
solve problems.
Concept Byte following 8-4:
Laws of Sines and Cosines
New CCSS
Focus on applying the Law of Sines
and Cosines. This standard will be
addressed at a deeper level in the
fourth math course.
Honors: Include the ambiguous case
of Law of Sines.
G.SRT.11 (+) Understand and apply
the Law of Sines and the Law of
Cosines to find unknown
measurements in right and non-right
triangles (e.g., surveying problems,
resultant forces).
8-5 Vectors
Prior Knowledge
Solve ratios and proportions, Pythagorean Theorem
3
New CCSS
CMS Curriculum Guides 2011-2012
Course Title Geometry
Key Vocabulary
Ratio
Proportion
Similar polygons
Scale factor
Pythagorean Triple
Trigonometric ratios
Sine
Cosine
tangent
Angle of depression
Angle of elevation
Vector
Initial point
Terminal point
Magnitude
Additional Online Resources
 Resources
Pearson Geometry Text: http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-368863-101/index.html

Inquiry Activities
TI nspire:
http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5024&t=5053&id=13151
Pythagorean Triples (expert) G.SRT.5 http://map.mathshell.org/materials/download.php?fileid=812
Rubric for Pythagorean Triples http://map.mathshell.org/materials/download.php?fileid=813

Problem-Based Task
Security Camera http://map.mathshell.org/materials/download.php?fileid=798
Security Camera Rubric http://map.mathshell.org/materials/download.php?fileid=799
Proof of the Pythagorean Theorem (expert) G.SRT.4
http://map.mathshell.org/materials/download.php?fileid=804
Rubric for Proof of the Pythagorean Theorem
http://map.mathshell.org/materials/download.php?fileid=805
Hopewell Geometry (apprentice) G.MG.3 http://map.mathshell.org/materials/download.php?fileid=499
Rubric for Hopewell Geometry http://map.mathshell.org/materials/download.php?fileid=500

Projects
Rep-tles http://mathforum.org/pom/sols3.96.html
Pearson Chapter 8 Project
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