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Questions and Answers
What does 'If a=b, then a+c=b+c' represent?
What does 'If a=b, then a+c=b+c' represent?
Addition
What does 'If a=b, then a-c=b-c' represent?
What does 'If a=b, then a-c=b-c' represent?
Subtraction
What does 'If a=b, then a times c=b times c' represent?
What does 'If a=b, then a times c=b times c' represent?
Multiplication
What does 'If a=b and c≠0, then a/c=b/c' represent?
What does 'If a=b and c≠0, then a/c=b/c' represent?
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What does 'a=a' represent?
What does 'a=a' represent?
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What does 'If a=b, then b=a' represent?
What does 'If a=b, then b=a' represent?
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What does 'If a=b and b=c, then a=c' represent?
What does 'If a=b and b=c, then a=c' represent?
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What does 'If a=b, then a may be replaced by b in any equation or expression' represent?
What does 'If a=b, then a may be replaced by b in any equation or expression' represent?
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What does 'a(b+c)=ab+ac' represent?
What does 'a(b+c)=ab+ac' represent?
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What is the Segment Addition Postulate?
What is the Segment Addition Postulate?
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What does 'A͞B ≅ A͞B' represent?
What does 'A͞B ≅ A͞B' represent?
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What does 'If A͞B ≅ C͞D, then C͞D ≅ A͞B' represent?
What does 'If A͞B ≅ C͞D, then C͞D ≅ A͞B' represent?
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What does 'If A͞B ≅ C͞D and C͞D ≅ E͞F, then A͞B ≅ E͞F' represent?
What does 'If A͞B ≅ C͞D and C͞D ≅ E͞F, then A͞B ≅ E͞F' represent?
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What does 'D is the interior of' represent?
What does 'D is the interior of' represent?
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Study Notes
Algebraic Proofs
- The Addition Property states: If a = b, then a + c = b + c.
- The Subtraction Property states: If a = b, then a - c = b - c.
- The Multiplication Property states: If a = b, then a × c = b × c.
- The Division Property states: If a = b and c ≠ 0, then a/c = b/c.
Properties of Equality
- The Reflexive Property indicates that a = a for any value a.
- The Symmetric Property asserts: If a = b, then b = a.
- The Transitive Property specifies: If a = b and b = c, then a = c.
- The Substitution Property allows for the replacement of a with b in any equation or expression if a = b.
Distributive Property
- The Distributive Property expresses that a(b + c) = ab + ac.
Segment Proofs
- The Segment Addition Postulate explains that if points A, B, and C are collinear, point B is between A and C if and only if AB + BC = AC.
Properties of Congruence
- The Reflexive Property of Congruence states: Segment AB is congruent to itself (AB ≅ AB).
- The Symmetric Property of Congruence maintains that if segment AB ≅ segment CD, then segment CD ≅ segment AB.
- The Transitive Property of Congruence specifies: If segment AB ≅ segment CD and segment CD ≅ segment EF, then segment AB ≅ segment EF.
Geometric Concepts
- Point D is defined as being in the interior of a segment or angle.
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Description
This quiz covers essential algebraic proofs including addition, subtraction, multiplication, and division properties. It also delves into reflexive properties and more. Test your understanding of fundamental algebraic concepts with these flashcards.
