Algebraic Proofs Examples Flashcards

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.

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.