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 List the Congruent sides and angles:. Unit Essential Question: How do you use given information to construct a proof involving congruent triangles?

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Presentation on theme: " List the Congruent sides and angles:. Unit Essential Question: How do you use given information to construct a proof involving congruent triangles?"— Presentation transcript:

1  List the Congruent sides and angles:

2 Unit Essential Question: How do you use given information to construct a proof involving congruent triangles?

3 Essential Question: When are triangles congruent?

4  Congruent Figures have the same size & shape. They can be transformed so that one will fit EXACTLY on the other:  Congruent figures have congruent corresponding parts.

5  If these triangles are congruent, then list the congruent corresponding parts:  Two triangles are congruent if all three pairs of sides and all three pairs of angles are congruent.

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7  Statements Reasons

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10  What does it mean to be SUFFICIENT?  Would having 3 pairs of congruent Angles be sufficient to GUARANTEE two triangles are congruent?  Why or Why not?

11 Essential Question: What are the sufficient conditions to prove triangles are congruent?

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15  INCLUDED?!?!

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20 Essential Question: What are the sufficient conditions to prove triangles are congruent?

21  Included side!!!

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28 Essential Question: How can you use congruent triangles to prove corresponding parts are congruent?

29  Once you know that a pair of triangles are congruent, you can safely concluded that ALL of the corresponding parts of these triangles must also be congruent:  Corresponding Parts of Congruent Triangles are Congruent, or CPCTC.

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34 Essential Questions: What does CPCTC reveal about Isosceles & Equilateral triangles?

35  Base  Legs  Vertex Angle  Base Angles

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42  What is the definition of congruent triangles?  What are sufficient conditions to prove triangles congruent?  How do you use CPCTC?

43 Essential Question: What are the sufficient conditions to prove triangles are congruent?

44  Hypotenuse  Legs

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46  Why isn’t it covered by SAS?  Need:  Two Right Triangles  Congruent Hypotenuses  Congruent Legs

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50 Essential Question: How can you use congruent triangles to prove corresponding parts are congruent?

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