Download 5 - Triangle Proofs File

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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?
Essential Question:
When are triangles congruent?
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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.

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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Statements
Reasons

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?
Essential Question:
What are the sufficient conditions to prove triangles are congruent?
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INCLUDED?!?!
Essential Question:
What are the sufficient conditions to prove triangles are congruent?

Included side!!!
Essential Question:
How can you use congruent triangles to prove corresponding
parts are congruent?

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.
Essential Questions:
What does CPCTC reveal about Isosceles & Equilateral triangles?
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Base
Legs
Vertex Angle
Base Angles

What is the definition of congruent triangles?

What are sufficient conditions to prove
triangles congruent?

How do you use CPCTC?
Essential Question:
What are the sufficient conditions to prove triangles are congruent?

Hypotenuse

Legs

Why isn’t it covered by SAS?

Need:
 Two Right Triangles
 Congruent Hypotenuses
 Congruent Legs
Essential Question:
How can you use congruent triangles to prove corresponding parts are
congruent?