Checking for Identical Triangles

Examples, videos, and solutions to help Grade 7 students learn how to use information such as vertical angles and common sides in the structure of triangle diagrams to establish whether conditions that determine a unique triangle exist.

New York State Common Core Math Grade 7, Module 6, Lesson 14

Worksheets for 7th Grade, Module 6, Lesson 14 (pdf)

Lesson 14 Student Outcomes

• Students use information such as vertical angles and common sides in the structure of triangle diagrams to establish whether conditions that determine a unique triangle exist.
• 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 14 Summary

• In deciding whether two triangles are identical, examine the structure of the diagram of the two triangles to look for a relationship that might reveal information about corresponding parts of the triangles. This information may determine whether the parts of the triangle satisfy a particular condition, which might determine whether the triangles are identical.

Lesson 14 Classwork

Opening Exercise
In each of the following problems, determine whether the triangles are identical, not identical, or whether they are not necessarily identical; justify your reasoning. If the relationship between the two triangles yields information that establishes a condition, describe the information. If the triangles are identical, write a triangle correspondence that matches the sides and angles.

Example 1
What is the relationship between the two triangles below?
Exercises 1–2
Are the triangles identical? Justify your reasoning.

Example 2
Are the triangles identical? Justify your reasoning. sides and included angle condition for identical triangles.
Exercises 3–7
Are the triangles identical? Justify your reasoning.

8. Create your own labeled diagram and set of criteria for a pair of triangles. Ask a neighbor to determine whether the triangles are identical based on the provided information.

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