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Module 2: Similarity, proof, and trigonometry

Topic A: Scale drawings

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Topic A: No content yet
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Topic B: Dilations

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Performing dilations
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Dilating shapes: expanding
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Dilating shapes: shrinking
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Lessons 10-11: No content yet
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Practice
Dilate pointsGet 3 of 4 questions to level up!
Dilations: scale factorGet 3 of 4 questions to level up!
Dilations: centerGet 3 of 4 questions to level up!
Dilate trianglesGet 3 of 4 questions to level up!
Dilations and propertiesGet 3 of 4 questions to level up!

Topic C: Lessons 12-14: Similarity intro

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Similar shapes & transformations
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Proof: all circles are similar
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Similarity & transformationsGet 3 of 4 questions to level up!
Sequences of transformationsGet 3 of 4 questions to level up!

Topic C: Lessons 15-17: Triangle similarity

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Intro to triangle similarity
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Triangle similarity postulates/criteria
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Determining similar triangles
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Solving similar triangles
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Solving similar triangles: same side plays different roles
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Practice
Determine similar triangles: AAGet 3 of 4 questions to level up!
Determine similar triangles: SSSGet 3 of 4 questions to level up!
Solve similar triangles (basic)Get 3 of 4 questions to level up!
Solve similar triangles (advanced)Get 3 of 4 questions to level up!

Topic C: Lessons 18-20: Similarity applications

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Intro to angle bisector theorem
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Using the angle bisector theorem
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Using similar & congruent triangles
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Challenging similarity problem
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Geometry word problem: the golden ratio
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Geometry word problem: Earth & Moon radii
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Geometry word problem: a perfect pool shot
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Practice
Solve triangles: angle bisector theoremGet 3 of 4 questions to level up!
Use similar & congruent trianglesGet 3 of 4 questions to level up!

Topic D: Applying similarity to right triangles

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Lesson 21: No content yet
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Simplifying square roots
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Simplifying square roots (variables)
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Simplifying square-root expressions
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Pythagorean theorem proof using similarity
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Practice
Simplify square rootsGet 3 of 4 questions to level up!
Simplify square roots (variables)Get 3 of 4 questions to level up!
Simplify square-root expressionsGet 3 of 4 questions to level up!

Topic E: Lessons 25-26: Trigonometry intro

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Intro to the trigonometric ratios
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Trigonometric ratios in right triangles
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Hypotenuse, opposite, and adjacent
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Trigonometric ratios in right triangles
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Triangle similarity & the trigonometric ratios
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Solving for a side in right triangles with trigonometry
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Solving for a side in right triangles with trigonometry
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Practice
Trigonometric ratios in right trianglesGet 3 of 4 questions to level up!
Solve for a side in right trianglesGet 3 of 4 questions to level up!

Topic E: Lesson 27: Sine and cosine of complementary angles and special angles

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Sine & cosine of complementary angles
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Using complementary angles
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Trig word problem: complementary angles
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Special right triangles intro (part 1)
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Special right triangles intro (part 2)
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30-60-90 triangle example problem
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Special right triangles proof (part 1)
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Special right triangles proof (part 2)
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Practice
Special right trianglesGet 5 of 7 questions to level up!

Topic E: Lesson 34: Unknown angles

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Intro to inverse trig functions
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Practice
Solve for an angle in right trianglesGet 3 of 4 questions to level up!

Topic E: Lessons 28-31: Trigonometry applications

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Right triangle word problem
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Angles of elevation and depression
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Lessons 30-31: No content yet
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Right triangle word problemsGet 3 of 4 questions to level up!

Topic E: Lessons 32-33: Laws of sines and cosines

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Solving for a side with the law of sines
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Solving for an angle with the law of sines
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Proof of the law of sines
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Solving for a side with the law of cosines
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Solving for an angle with the law of cosines
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Proof of the law of cosines
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Trig word problem: stars
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Practice
Solve triangles using the law of sinesGet 3 of 4 questions to level up!
Solve triangles using the law of cosinesGet 3 of 4 questions to level up!
General triangle word problemsGet 3 of 4 questions to level up!

About this unit

"Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2. To be able to discuss similarity, students must first have a clear understanding of how dilations behave. This is done in two parts, by studying how dilations yield scale drawings and reasoning why the properties of dilations must be true. Once dilations are clearly established, similarity transformations are defined and length and angle relationships are examined, yielding triangle similarity criteria. An in-depth look at similarity within right triangles follows, and finally the module ends with a study of right triangle trigonometry." Eureka Math/EngageNY (c) 2015 GreatMinds.org