Geometry

Lesson 14

Objective

Identify unique and identical triangles. 

Common Core Standards

Core Standards

?

  • 7.G.A.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Criteria for Success

?

  1. Understand that the location and adjacency of angles and side lengths can determine identical or different triangles. 
  2. Identify identical copies of the same triangle.
  3. Sketch drawings of the same triangle in different orientations.

Tips for Teachers

?

In Lessons 14 and 15, students investigate the situations that create unique, more than one, or no triangle. In this lesson, students observe how the conditions described about a triangle can sometimes be represented in a diagram in different ways. They will begin to sketch triangles with given conditions and continue this in Lesson 15. 

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example) and Anchor Problem 2 (benefits from discussion). Find more guidance on adapting our math curriculum for remote learning here.

Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package

 

Anchor Problems

?

Problem 1

Examine this set of triangles.

  1. What is the same about the triangles in the set? What is different?
  2. How many different triangles are there? Explain or show your reasoning. 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Open Up Resources Grade 7 Unit 7Lesson 8.2 - 2 Sides and 1 Angle

Grade 7 Unit 7 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 11, 2018, 12:12 p.m..

Problem 2

Phil, Raul, and Teresa each drew a right triangle with another angle measuring 30° and a side length of 4 inches. Their drawings are shown below (not drawn to scale). 

Phil claims that he drew the same triangle as Raul, but different from Teresa. Do you agree with Phil? Explain why or why not.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

?

With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include problems where students are given a set of triangles with the same measurements and must determine which triangles are the same but in different orientations and which triangles are different.

Target Task

?

A triangle has side lengths 8 cm and 3 cm and one angle that measures 20°.

  1. Draw and label two triangles that have the measurements above and are the same triangle. 
  2. Draw and label a triangle that has the measurements above but is different from the triangle you drew in part (a). 

Mastery Response

?

Create a free account or sign in to view Mastery Response