Algebra Class 2-6 to 2-8 Proofs Flashcards

Questions and Answers

What does 'If a=b, then a+c=b+c' represent?

Addition

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?

Multiplication

What does 'If a=b and c≠0, then a/c=b/c' represent?

Division Signup and view all the answers

What does 'a=a' represent?

Reflexive Signup and view all the answers

What does 'If a=b, then b=a' represent?

Symmetric Signup and view all the answers

What does 'If a=b and b=c, then a=c' represent?

Transitive Signup and view all the answers

What does 'If a=b, then a may be replaced by b in any equation or expression' represent?

Substitution Signup and view all the answers

What does 'a(b+c)=ab+ac' represent?

Distributive Signup and view all the answers

What is the Segment Addition Postulate?

If A, B, and C are collinear, then point B is between point A and C if and only if AB+BC=AC. Signup and view all the answers

What does 'A͞B ≅ A͞B' represent?

Reflexive Property of Congruence Signup and view all the answers

What does 'If A͞B ≅ C͞D, then C͞D ≅ A͞B' represent?

Symmetric Property of Congruence Signup and view all the answers

What does 'If A͞B ≅ C͞D and C͞D ≅ E͞F, then A͞B ≅ E͞F' represent?

Transitive Property of Congruence Signup and view all the answers

What does 'D is the interior of' represent?

Incomplete statement Signup and view all the answers

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.

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.