Questions and Answers
What does CPCTC mean?
Corresponding parts of congruent triangles are congruent.
Why must you show in your proof before using CPCTC?
Two triangles are congruent.
What do you use CPCTC for in a proof?
To prove the additional sides or angles are congruent.
What does HL stand for?
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What does SAS stand for?
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What does AAS stand for?
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What does SSS stand for?
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What does ASA stand for?
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What is a midpoint?
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What is a segment bisector?
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What is an angle bisector?
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Vertical angles are congruent.
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All right angles are congruent.
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The corresponding parts of congruent triangles are?
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Study Notes
CPCTC Overview
- CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent."
- This theorem is crucial in geometry for proving that specific angles or sides in triangles are congruent.
Proof Requirements
- Before applying CPCTC in a proof, it is essential to demonstrate that the two triangles in question are congruent.
Purpose of CPCTC
- Used in geometric proofs to establish that additional sides or angles are congruent based on the congruence of triangles.
Key Triangle Congruence Theorems
- HL (Hypotenuse-Leg): Applies to right triangles having one pair of congruent hypotenuses and one pair of congruent legs.
- SAS (Side-Angle-Side): Involves triangles with two pairs of congruent sides and one pair of included angles that are congruent.
- AAS (Angle-Angle-Side): Refers to triangles having two pairs of congruent angles and one pair of non-included sides congruent.
- SSS (Side-Side-Side): Used for triangles where all three pairs of sides are congruent.
- ASA (Angle-Side-Angle): Involves triangles with two pairs of congruent angles and one pair of included sides congruent.
Segment and Angle Definitions
- Midpoint: A point that divides a segment into two equal (congruent) segments.
- Segment Bisector: A line that splits a segment into two congruent segments.
- Angle Bisector: A line or ray that divides an angle into two congruent angles.
Angle Properties
- Vertical angles are always congruent.
- All right angles are congruent, emphasizing the equality of their measures.
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Description
Test your understanding of CPCTC in geometry with these flashcards. Learn the meanings, applications, and requirements for using CPCTC in triangle congruence proofs. Perfect for students looking to strengthen their knowledge of geometric proofs.
