Progressive Mathematics Initiative
www.njctl.org
Mathematics Curriculum
Unit Plan # 4
Title: Triangles
Subject: Geometry
Length of Time: 3 weeks
Unit Summary: In this unit, students learn to classify triangles by their sides and angles, as well as the
Triangle Sum Theorem. Then, they will be comparing the lengths of sides or the measures of angles of a
triangle using the Triangle Inequality Theorem. The unit concludes with the ways in which to prove figures
are similar and the proportions that result from similar figures.
Learning Targets
PARCC
Major Clusters;
Supporting Clusters;
Additional Clusters
Conceptual Category: Geometry Domain: Congruence
Cluster: Prove geometric theorems
Standard#:
G-CO.9
Standard#:
G-CO.10
Standard:
Points on a perpendicular bisector of a segment are exactly those equidistant from the
segment’s endpoints.
Standard:
Prove theorems about midsegment, medians, and triangles.
Cluster: Prove theorems involving similarity
Standard#:
Standard:
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle
G-SRT.4
divides the other two proportionally.
Use congruence and similarity criteria for triangles to solve problems and to prove
G-SRT.5
relationships in geometric figures.
Cluster: Apply geometric concepts in modeling situations.
Standard#:
Standard:
Apply geometric methods to solve design problems (working with typographic grid systems
G-MG.3
based on ratios).
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:
 How can statements about triangles
 Classifying triangles by sides and angles
be proven?
 The sum of the angles of a triangle is 1800
 Triangle Inequalities
 Similarity statements for triangles
 Proofs involving similar triangles
Unit Objectives:
 Students will be able to identify triangles by sides and angles
 Students will be able to write and solve algebraic equations to find the missing angle measurement,
Geometry: Triangles
~1~
NJCTL.org
and/or the value of the variable using the Triangle Sum Theorem and Exterior Angles Theorem.
Students will be able to identify which side of a triangle is the largest, knowing angle measure.
Students will be able to identify which angle is the largest, knowing side lengths.
Students will be able to write and solve proportions to find the missing side lengths in similar
triangles.
 Students will be able to determine whether or not triangles are similar based on the given
information.
 Students will be able to construct arguments and/or reasons to prove that triangles are similar.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 4 Quizzes
Summative Assessment:
 Unit Test
Lesson Plan
Topics
Days
Topic #1: Classifying Triangles
1



Topic #2: Interior Angle Theorems
1
Lab 1: Triangle Sum Theorem
Topic #3: Exterior Angle Theorems
1
Quiz 1 Classifying Triangles, Triangle Angle
0.5
Theorem, & Exterior Angle Theorem
Topic #4: Triangle Inequalities
2.5
Lab 2: Inequalities in One-Triangle
Lab 3: Triangle Inequality
Quiz 2: Triangle Inequalities
0.5
Topic #5: Similar Triangles
5
Lab 4: What does lengths of corresponding sides
(Slides 3 days
are proportional mean?
Labs each ½ day)
Lab 5: Angle-Angle Similarity Lab
Lab 6: Side-Side-Side Similarity Lab
Lab 7: Side-Angle-Side Similarity Lab
Quiz 3: Similar Triangles
1
Topic #7: Review and Unit Test
2
Curriculum Resources:
 www.njctl.org/courses/math/geometry/
 Geometer’s Sketchpad Labs and Investigations are posted to the website and noted in the presentation
file.
Lesson Components
21st Century Skills
 Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Themes
 Critical Thinking and Problem Solving
 Communication and Collaboration
 Life and Career Skills
Geometry: Triangles
~2~
NJCTL.org