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Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 2

This single-day resources gives students an opportunity to deepen their understanding of trigonometry, special triangles, while giving them a preview of area.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
activity
Standards
Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
+— Details
Common Core: Major Standards:
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.★

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Dilating Lines: An Exploration
Resource:
Dilating Lines: An Exploration

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 1

These student worksheets have the students use slope and distance to dilate a line.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Standards
Common Core: Major Standards ( G-SRT.B.4, G-SRT.B.5 ) Common Core: Additional S…
+— Details
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.

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.★

All Resources From:
End of Unit Assessment (Geometry, Unit 4)
Geometry & Algebra II Archive
Geo U4: Right Triangle Trigonometry
Resource:
End of Unit Assessment (Geometry, Unit 4)

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

End of Unit Assessment: End of Unit Assessment for Unit 4

After this unit, how prepared are your students for the end-of-course Regents examination?  The end of unit assessment is designed to surface how students understand the mathematics in the unit.  It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.  A rich task, that allows for multiple entry points and authentic assessment of student learning, may be available for some units and can be included as part of the end of unit assessment.  All elements of the end of unit assessment are aligned to the NYS Mathematics Learning Standards and PARCC Model Frameworks prioritization. 

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Geometry: Right Triangle Trigonometry
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End of Unit Assessment
All Resources From:
End of Unit Assessment Teacher Resources (Geometry, Unit 4)
Resource:
End of Unit Assessment Teacher Resources (Geometry, Unit 4)

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Geometry: Right Triangle Trigonometry
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End of Unit Assessment
Example Proofs of the Pythagorean Theorem
Resource:
Example Proofs of the Pythagorean Theorem

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 1

Website that models different proofs of the Pythagorean theorem, with diagrams.

Open Resource
Type
Geometry: Right Triangle Trigonometry
File
External Link
Tags
pythagorean theorem, triangle
Standards
Common Core: Major Standards ( G-SRT.B.4, G-SRT.B.5 ) Common Core: Additional S…
+— Details
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.

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.★

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Finding the Height of Your School
Resource:
Finding the Height of Your School

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 2

Using right triangle trigonometry, students will be able to find the height of the school building.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
right, triangle, trigonometry
Standards
Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
+— Details
Common Core: Major Standards:
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.★

All Resources From:
How to Build a Soccer Goal
Resource:
How to Build a Soccer Goal

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 2

Resources that can be used to apply the Pythagorean Theorem to the construction of a soccer goal from cylindrical piping.

Open Resource
Type
Geometry: Right Triangle Trigonometry
File
External Link
Tags
cylinder, pythagorean theorem
Standards
Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
+— Details
Common Core: Major Standards:
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.★

All Resources From:
Instructions for Hopewell Geometry
Geometry & Algebra II Archive
Geo U4: Right Triangle Trigonometry
Resource:
Instructions for Hopewell Geometry

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Initial Task: Hopewell Geometry

This page contains instructions on how to use the initial task, Hopewell Geometry, to find out what your students already know about reasoning with right triangles.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
Initial task
All Resources From:
Introducing Right Triangles
Resource:
Introducing Right Triangles

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 2

The objective for this initial introduction is to motivate the use of right-angle trigonometry through an investigation followed by a problem solving task using the results of that investigation.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
activity
Standards
Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
+— Details
Common Core: Major Standards:
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.★

All Resources From:
Parallax
Resource:
Parallax

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 2

Students will use distant buildings and the changing angles as they move in 1 direction to apply trig and find missing distances.

Preview ResourceAdd a Copy of Resource to my Google Drive
Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
trigonometry, right, triangles
Standards
Common Core: Major Standards ( G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 ) Common Core: A…
+— Details
Common Core: Major Standards:
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.★

All Resources From:
Proofs of the Pythagorean Theorem
Resource:
Proofs of the Pythagorean Theorem

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Formative Assessment Lesson: Proofs of the Pythagorean Theorem

A Classroom Challenge (aka formative assessment lesson) is a classroom-ready lesson that supports formative assessment. The lesson’s approach first allows students to demonstrate their prior understandings and abilities in employing the mathematical practices, and then involves students in resolving their own difficulties and misconceptions through structured discussion.

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Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Tags
formative assessment
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Proving the Pythagorean Theorem
Resource:
Proving the Pythagorean Theorem

Geometry & Algebra II Archive

Geo U4: Right Triangle Trigonometry

Big Idea: Big Idea 1

<style type="text/css"><!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> </style> During this Core Resource, students explore the Pythagorean theorem and how similar triangles can be used in a variety of different ways to prove theorems about right triangles, including the Pythagorean theorem itself.

Preview ResourceAdd a Copy of Resource to my Google Drive
Type
Geometry: Right Triangle Trigonometry
File
Google Doc
Standards
Common Core: Major Standards ( G-SRT.B.4, G-SRT.B.5 ) Common Core: Additional S…
+— Details
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.

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.★

All Resources From: