Right Triangle Trigonometry

8 Components
Initial Task
Hopewell Geometry
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Proofs of the Pythagorean Theorem
Re-engagement
Re-engagement for Unit 4
End of Unit Assessments
End of Unit Assessment for Unit 4 End of Unit Assessment Teacher Resources for GEO Unit 4 Find aligned Regents questions with Quiz Banker
Geo U4: Right Triangle Trigonometry
Unit Outline
Initial Task
Hopewell Geometry
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Proofs of the Pythagorean Theorem
Re-engagement
Re-engagement for Unit 4
End of Unit Assessments
End of Unit Assessment for Unit 4 End of Unit Assessment Teacher Resources for GEO Unit 4 Find aligned Regents questions with Quiz Banker
None
Geo U4:

Right Triangle Trigonometry

What relationships exist between the sides of similar right triangles?
4 weeks
See Standards
Common Core: Major Standards:
G-SRT.B.4

Prove theorems involving similarity. Prove theorems about triangles. 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. Clarification: Theorems include but are not limited to the listed theorems. Example: the length of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the lengths of the two segments of the hypotenuse.

G-SRT.B.5

Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Clarification: ASA, SAS, SSS, AAS, and Hypotenuse-Leg theorem are valid criteria for triangle congruence. AA, SAS, and SSS are valid criteria for triangle similarity.

G-SRT.C.6

Define trigonometric ratios and solve problems involving right triangles. 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.

G-SRT.C.7

Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles.

G-SRT.C.8

Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★

Common Core: Additional Standards:
G-GMD.A.1

Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

G-GMD.A.3

Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

Unit four is about right triangles and the relationships that exist between its sides and angles. Students apply their understanding of similarity, from unit three, to prove the Pythagorean Theorem. Trigonometric functions, which are properties of angles and depend on angle measure, are also explained using similarity relationships. Students determine when to use trigonometric ratios, Pythagorean Theorem, and/or properties of right triangles to model problems and solve them. Throughout the unit, students should be applying similarity and using inductive and deductive reasoning as they justify and prove these right triangle relationships.

Essential Questions:

  • What relationships exist between the sides of similar right triangles?
  • What is the relationship between angles and sides of a right triangle?
Printable Unit Plan
  • Geometry Unit Plan for Unit 4
    Resource:
    Geometry Unit Plan for Unit 4

    This is a printable version of the entire unit plan. You can make a copy of it and edit it or download and print it as needed.

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Unit Outline

8 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 2 itemsHide 2 items

Formative Assessment Lesson See 1 itemHide 1 item

Re-engagement See 1 itemHide 1 item

End of Unit Assessments See 3 itemsHide 3 items