2-2: from Algebra and Two-Column Proofs! Conditional: If 2 coplanar lines are parallel, then they do not intersect. T/F? Converse: Biconditional: of Algebra Use p. 37-38 to help you identify the algebraic property. 1. If 5π₯β 3 = 27, then 5π₯ = 30. 2. If π§ = 7 and π¦ = 7, then π§ = π¦. 3. 10(π₯ + 7) = 10π₯ + 70. 4. If 18π₯ = 36, then π₯ = 2. 5. If π¦ = 3π₯ + 7 and π₯ = 2, then π¦ = 3(2) + 7. 6. ππ β ππ. Addition Property of Equality Adding the same number to both sides of an equation keeps the equation true. Add. Prop. of = If π = π, then π + π = π + π Multiplication Property of Equality Multiplying the same number by both sides of an equation keeps the equation true. Mult. Prop. of = If π = π, then π · π = π · π Reflexive Property of Equality Relf. Prop. of = Any value (number) is equal to itself. π=π Symmetric Property of Equality Sym. Prop. of = The two sides of an equation can be written in either order. If π = π, then π = π Transitive Property of Equality Two values that are both equal to a third value must be equal to each other. Trans. Prop. of = If π = π, and π = π then π = π Substitution Property of Equality Any value can be replaced (substituted) by any value equal to it. Subs. Prop. of = If π = π, then π can replace π in any expression Distributive Property Dist. Prop. A number that multiplies a sum can multiply each term in the sum. π π+π =π·π+π·π Reflexive Property of Congruence Any geometric figure that can be measured is congruent to itself. Refl. Prop. of β β π β β π π¨π© β π¨π© Symmetric Property of Congruence The two sides of a congruence statement can be written in either order. Sym. Prop. of β If β π β β π, then β π β β π If π¨π© β πͺπ«, then πͺπ« β π¨π© Transitive Property of Congruence Two geometric figures that are both congruent to a third figure must be congruent to each other. Trans. Prop. of β If β π β β π, and β π β β π, then β π β β π 2-Column Proofs Step-by-step logic Justify each step Statements Reasons Algebra Examples Given: π π + π = π + ππ, π = 1 Statements Prove: π = π . Reasons Algebra Examples Given: π = π + π, π < 0 Statements Prove: π < π Reasons Geometry Time! Given: πβ 1 = πβ 3, mβ 2 = πβ 4 Statements Prove: πβ π΄π΅πΆ = πβ π·πΈπΉ Reasons π΄ 1 π΅ 2 πΆ πΉ 4 3 π· πΈ Geometry Time! Given: π π = πΌπ, π π = ππ Reasons π π π β β Statements Prove: ππ = ππΌ π πΌ π p. 41: 1-13 odd You should be copying all diagrams on homework assignments
© Copyright 2026 Paperzz