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Understanding Congruent Triangles through Transformations

This learning module focuses on how to apply properties of transformations to determine triangle congruence. Students will explore the concept of corresponding sides and angles, learn to visually identify pairs, and assess if having only one or two pairs of corresponding elements is sufficient to prove congruence. Collaborative discussions will encourage students to formulate explanations and understand the implications of limited information on triangle congruence. Engaging with these concepts will deepen understanding of geometric transformations and congruence criteria in triangles.

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Understanding Congruent Triangles through Transformations

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  1. Minimum Measurement Congruent Triangles

  2. Learning Goal 2(8.G.A.2, 8.G.A.3): Apply properties of transformations to perform and explain sequences of transformations and prove figures are congruent.

  3. What does “corresponding” mean? • Corresponding sides or angles means that the side or angle appears in the same place in the other figure. • How do you visually recognize the corresponding pairs of sides? • Which side of ΔPQR should match segment AC? Explain how you know. • Which angle is the largest angle in ΔABC? Where is the corresponding angle in ΔPQR located?

  4. Is there enough information? • Can you be sure that two triangles are congruent if you know that there is only one pair of corresponding sides are congruent? • Work with a partner to come up with an explanation to prove this is true or prove it is not. • Not enough information:

  5. Is there enough information? • Can you be sure that two triangles are congruent if you know that there is only one pair of corresponding angles are congruent? • Work with a partner to come up with an explanation to prove this is true or prove it is not. • Not enough information:

  6. Is there enough information? • Can you be sure that two triangles are congruent if you know that there is only two pairs of corresponding sides are congruent? • Work with a partner to come up with an explanation to prove this is true or prove it is not. • Not enough information:

  7. Is there enough information? • Can you be sure that two triangles are congruent if you know that there is only two pairs of corresponding angles are congruent? • Work with a partner to come up with an explanation to prove this is true or prove it is not. • Not enough information:

  8. Is there enough information? • Can you be sure that two triangles are congruent if you know that there is one pair of corresponding angles that are congruent and one pair of corresponding sides that are congruent? • Work with a partner to come up with an explanation to prove this is true or prove it is not. • Not enough information:

  9. Use Labsheet 2.3 to complete the activity.

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