Podcast
Questions and Answers
What does CPCTC mean?
What does CPCTC mean?
corresponding parts of congruent triangles are congruent
Does ASA prove congruence?
Does ASA prove congruence?
True
Does SAS prove congruence?
Does SAS prove congruence?
True
Does SSS prove congruence?
Does SSS prove congruence?
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Does AAS prove congruence?
Does AAS prove congruence?
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Does SSA prove congruence?
Does SSA prove congruence?
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What does a flowchart proof need to have?
What does a flowchart proof need to have?
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What is the CPCTC theorem?
What is the CPCTC theorem?
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Study Notes
CPCTC Overview
- CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent".
- This theorem is essential in triangle congruence and proves that specific parts of triangles are equal when the triangles themselves are congruent.
Triangle Congruence Theorems
- ASA (Angle-Side-Angle) proves triangle congruence.
- SAS (Side-Angle-Side) also confirms triangle congruence.
- SSS (Side-Side-Side) is a valid method for establishing triangle congruence.
- AAS (Angle-Angle-Side) successfully demonstrates triangle congruence.
- SSA (Side-Side-Angle) does not guarantee congruence.
Flowchart Proof Requirements
- A flowchart proof requires three true statements that lead to a similarity statement.
- It must include a theorem justifying why the conclusions are true.
- Sometimes, it incorporates an extension for CPCTC to further validate the congruency of parts.
CPCTC Theorem Details
- If two triangles are proven congruent via ASA, SAS, SSS, or AAS, then all corresponding sides and angles are equal.
- CPCTC is significant for solving geometric problems involving congruent triangles, aiding in finding unknown angles and side lengths.
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