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Questions and Answers
What does 'Given' refer to in the context of algebraic proofs?
What does 'Definition of congruency' refer to in algebraic proofs?
What does 'Substitution property of equality' imply in algebraic proofs?
What does 'Subtraction property of equality' state?
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What does 'Addition property of equality' refer to?
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What does 'Division property of equality' state?
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What is implied by the 'Transitive property'?
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What does the 'Transitive property' suggest in congruency?
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What does the 'Definition of congruency' state in algebraic terms?
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What does the 'Symmetric property' indicate?
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Study Notes
Algebraic Proofs Fundamentals
- Given indicates the established facts, such as angles that are congruent, e.g., ∠ W ≅ ∠ Z.
Definition of Congruency
- Congruency definition involves the equality of angle measures, exemplified by m∠w = m∠c.
Substitution Property of Equality
- This property allows for the replacement of one expression with another equal expression, illustrated by the equation 11x - 8 = 9x + 4.
Subtraction Property of Equality
- This property states that if two expressions are equal, subtracting the same value from both sides maintains equality, demonstrated by 2x - 8 = 4.
Addition Property of Equality
- When both sides of an equation are increased by the same amount, equality is preserved, seen in the equation 2x = 12.
Division Property of Equality
- This principle allows dividing both sides of an equation by the same non-zero number, illustrated by the solution x = 6.
Transitive Property
- If two quantities are each equal to a third quantity, they are equal to each other, as seen with ∠ ABD ≅ ∠ EBC.
Transitive Property in Congruency
- Similar to equality, congruent segments or angles can be linked; for instance, if FG ≅ JH, then FG and JH are congruent.
Definition of Congruency in Measurements
- The measure of congruent segments or angles are equal, e.g., FG = JH signifies the equality of length or angle measure.
Symmetric Property
- This property states that if one quantity equals another, the second quantity equals the first; showcased by the transition from 4 = x to x = 4.
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Description
Test your understanding of algebraic proofs with this flashcard quiz. Each card presents a key concept or property related to congruency and equality used in algebraic proofs. Review definitions and identify the steps to strengthen your knowledge in algebra.