Progressive Mathematics Initiative
www.njctl.org
Mathematics Curriculum
Unit Plan # 5
Title: Similar Triangles and Trigonometry
Subject: Geometry
Length of Time: 4 weeks
Unit Summary: The unit is an introduction to trigonometry. The unit begins with solving word problems
using similarity and indirect measurement. This leads to the derivation of the sine, cosine, and tangent
ratios, including word problems. The unit concludes with the Pythagorean Theorem and its converse, as
well as the ratios of 30-60-90 and 45-45-90 and solving problems with those ratios.
Learning Targets
PARCC
Major Clusters;
Supporting Clusters;
Additional Clusters
Conceptual Category: Geometry Domain: Similarity, Right Triangles, and Trigonometry
Cluster: Prove theorems using similarity
Standard#:
Standard:
Prove theorems about triangles.
G-SRT.4
Cluster: Define trigonometric ratios and solve problems involving right triangles
Understand that by similarity, side ratios in right triangles are properties of the angles in
G-SRT.6
the triangle, leading to definitions of trigonometric ratios for acute angles.
Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.7
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
G-SRT.8
problems.
Domain: Standards for Math Practice
Standard#:
Standard:
MP1
Making sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
MP4
Model with mathematics.
MP5
Use appropriate tools strategically.
MP6
Attend to precision.
MP7
Look for and make use of structure.
MP8
Look for and express regularity in repeated reasoning.
Unit Essential Question:
Unit Enduring Understandings:
 What is the relationship between the
 Pythagorean Theorem
sides and angles of right triangles?
 Sine, Cosine, and Tangent
 30-60-90 Triangle Theorem
 45-45-90 Triangle Theorem
Unit Objectives:
 Students will be able to use similarity ratios to solve problems.
 Students will be able to use trigonometric ratios to solve right triangles.
 Students will be able to derive the trigonometry formulas.
 Students will be able to solve problems and identify right triangles using Pythagorean Theorem.
 Students will be able to derive the 45-45-90 & 30-60-90 triangle theorems.
 Students will be able to solve problems using the 45-45-90 & 30-60-90 triangle theorems.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 5 Quizzes
Geometry – Similar Triangles & Trig
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NJCTL.org
 3 Labs
Summative Assessment:
 Unit Test
Lesson Plan
Topics
Topic #1: Problem Solving w/ Similar Triangles
Lab #1: Indirect Measurement
Quiz#1: Problem Solving w/ Similar Triangles
Topic #2: Similar Triangles & Trigonometry
Lab #2: Finding Trigonometric Ratios
Topic #3: Trigonometric Ratios
Quiz#2: Trigonometry
Topic #4: Inverse Trigonometric Ratios
Quiz #3: Inverse Trigonometric Ratios
Lab #3: WebQuest: Right Triangles & Stairs
2
1
0.5
1
1
3
1
2
0.5
1 day to introduce; give students 1-2 weeks to
complete on their own
1
1
0.5
2
0.5
2
Topic #5: Review of the Pythagorean Theorem
Topic #6: Converse of the Pythagorean Theorem
Quiz #4: Pythagorean Theorem & Its Converse
Topic #6: Special Right Triangles
Quiz #5: Special Right Triangles
Topic #7: Sample PARCC Q’s, Review and Unit
Test
Curriculum Resources:
 www.njctl.org/courses/math/geometry/
 WebQuest: Right Triangles & Stairs: www.alschappell.net/WQStairs/WQStairs.htm
o Note: Please send any additional feedback from the conclusion essay about the WebQuest to
http://www.njctl.org/courses/math/geometry-2015-16/similar-triangles-trigonometry/
Lesson Components
21st Century Skills
 Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Themes
 Critical Thinking and Problem Solving
 Communication and Collaboration
 Creativity & Innovation
 ICT Literacy
 Life and Career Skills
Geometry – Similar Triangles & Trig
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NJCTL.org