Checking for Identical Triangles

Examples, videos, and solutions to help Grade 7 students learn how to use conditions that determine a unique triangle to determine when two triangles are identical.

New York State Common Core Math Grade 7, Module 6, Lesson 13

Worksheets for 7th Grade, Module 6, Lesson 13 (pdf)

Lesson 13 Student Outcomes

• Students use conditions that determine a unique triangle to determine when two triangles are identical.
• Students construct viable arguments to explain why the given information can or cannot give a triangle correspondence between identical triangles.

Lesson 13 Summary

• The measurement and arrangement (and correspondence) of the parts in each triangle plays a role in determining whether two triangles are identical.

Lesson 13 Classwork

Opening Exercise
a. List all the conditions that determine unique triangles:
b. How are the terms identical and unique related?

In each of the following problems, two triangles are given. State whether the triangles are identical, not identical, or not necessarily identical. If possible, give the triangle conditions that explain why the triangles are identical, and write a triangle correspondence that matches the sides and angles. If the triangles are not identical, explain why. If it is not possible to definitively determine whether the triangles are identical, write “the triangles are not necessarily identical,” and explain your reasoning.

In Example 2 and Exercises 4–6, three pieces of information are given for △ABC and △XYZ. Draw, freehand, the two triangles (do not worry about scale), and mark the given information. If the triangles are identical, give a triangle correspondence that matches equal angles and equal sides. Explain your reasoning.

Exercises 4 - 6.

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