These Triangle Aren’t Congruent… Are They?

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Presentation transcript:

These Triangle Aren’t Congruent… Are They?

Essential Questions Is knowing that two triangles have the same side lengths enough to be confident that those two triangles are congruent? What is the connection among translating, rotating, or reflecting two triangles so that they match up exactly, and knowing that those two triangles are the exact same size and shape?

Recap Lesson 1 What strategies did you use to find congruent halves? What did you look for to give you hints about where to draw the dividing line?

Re-cap Lesson 1 What strategies did you use to find congruent halves? What did you look for to give you hints about where to draw the dividing line?

How do you know two shapes are congruent?

Definition of Congruent Figures Two shapes are congruent if and only if there exists a sequence of rigid transformations that map one shape onto the other.

Two shapes are congruent if and only if there exists a sequence of rigid transformations that map one shape onto the other.

IF there exists a sequence of rigid transformations that map one shape onto the other THEN the two shapes are congruent. IF the two shapes are congruent THEN there exists a sequence of rigid transformations that map one shape onto the other.

What can you conclude? GIVEN: ABC is congruent to DEF.

What can you conclude? GIVEN: A’B’C’D’ is a rotation of ABCD around Point P.

Can you explain the difference between the two halves of the definition? IF there exists a sequence of rigid transformations that map one shape onto the other THEN the two shapes are congruent. IF the two shapes are congruent THEN there exists a sequence of rigid transformations that map one shape onto the other.

What can you conclude? Two triangles have side lengths 5 cm, 7 cm, and 9 cm and side lengths 7 cm, 5 cm, and 9 cm.

Conjecture: What conjecture could we make about triangle congruence?