Progressive Mathematics Initiativewww.njctl.org

Mathematics CurriculumUnit Plan # 3

Title: Triangles

Subject: Geometry Length of Time: 3.5 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

Conceptual Category: Geometry Domain: Congruence

Cluster: Prove geometric theorems

Standard#: Standard:G-CO.9 Points on a perpendicular bisector of a segment are exactly those equidistant from the

segment’s endpoints.Standard#: Standard:

G-CO.10 Prove theorems about midsegment, medians, and triangles.

Cluster: Prove theorems involving similarity

Standard#: Standard:

G-SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally.

G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Cluster: Apply geometric concepts in modeling situations.

Standard#: Standard:

G-MG.3 Apply geometric methods to solve design problems (working with typographic grid systems based on ratios).

Unit Essential Question: How can statements about triangles

be proven?

Unit Enduring Understandings: Classifying triangles by sides and angles 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,

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.

Geometry: Triangles ~1~ NJCTL.org

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: 4 Quizzes Unit Test

Lesson PlanTopics Days

Topic #1: Classifying Triangles 1

Topic #2: Interior Angle TheoremsLab 1: Triangle Sum Theorem

1

Topic #3: Exterior Angle Theorems 1Quiz 1 Classifying Triangles, Triangle Angle Theorem, & Exterior Angle Theorem

0.5

Topic #4: Triangle InequalitiesLab 2: Inequalities in One-TriangleLab 3: Triangle Inequality

3

Quiz 2: Triangle Inequalities 0.5Topic #5: Similar TrianglesLab 4: What does lengths of corresponding sides are proportional mean?Lab 5: Angle-Angle Similarity LabLab 6: Side-Side-Side Similarity LabLab 7: Side-Angle-Side Similarity Lab

7

Quiz 3: Similar Triangles 1Topic #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.

Geometry: Triangles ~2~ NJCTL.org