Untitled Quiz

Questions and Answers

What does CPCTC mean?

corresponding parts of congruent triangles are congruent

Does ASA prove congruence?

True

Does SAS prove congruence?

True

Does SSS prove congruence?

True Signup and view all the answers

Does AAS prove congruence?

True Signup and view all the answers

Does SSA prove congruence?

False Signup and view all the answers

What does a flowchart proof need to have?

three true facts coming to a similarity statement and a theorem for why it is true and (sometimes) another extension for CPCTC Signup and view all the answers

What is the CPCTC theorem?

CPCT stands for Corresponding Parts of Congruent Triangles. It means that if any two triangles are congruent by ASA, SAS, SSS, then their remaining sides and angles will also be equal. Signup and view all the answers

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.