Download 2.5 Reason Using Properties from Algebra

Geometry Chapter 2: Reasoning and Proof Section 2.5-­‐ Reason Using Properties from Algebra SWBAT: use algebraic properties in logical arguments. Common Core: A-­‐REI.1  ALGEBRAIC PROPERTIES OF EQUALITY Let a, b, and c, be real numbers. Addition Property: If a = b, then ___________________________________. Subtraction Property: If a = b, then __________________________________. Multiplication Property: If a = b, then _________________________________. Division Property: If a = b and c ≠ 0, then ______________________________. Substitution Property: If a = b, then _________________________________________________________. Example 1: Write reasons for each step Solve 2𝑥 + 3 = 9 − 𝑥. Write a reason for each step. Equation Explanation Reason 2x + 3 = 9 – x Write original equation. Given 2x + 3 + ______ = 9 – x + _______ Add __________ to each side. _____________________________________ ___________ + 3 = ___________ Combine like terms. ______________________________________ _________________ = ____________ Subtract _____________ from each side ______________________________________ x = ____________ Divide each side by __________________. ______________________________________ The value of x is ________________________. Geometry Chapter 2: Reasoning and Proof  DISTRIBUTIVE PROPERTY
a(b + c) =__________________________, where a, b, and c are real numbers. Example 2: Use the Distributive Property Solve −4 6𝑥 + 2 = 64. Write a reason for each step. Solution: Equation Explanation Reason -­‐4(6x + 2) = 64 Write original equation. Given ___________________________ = 64 Multiply ____________________________________ _________________ = ____________ Add _________ to both sides. _______________________ Property of Equality _________________ = _____________ Divide each side by _______________. _______________________ Property of Equality Practice: 1. Solve 𝑥 − 5 = 7 + 2𝑥. Write a reason for each step. Geometry Chapter 2: Reasoning and Proof 2. Solve 4 5 − 𝑥 = −2𝑥. Write a reason for each step. Example 3: Use Properties in the Real World A motorist travels 5 miles per hour slower than the speed limit s for 3.5 hours. The distance traveled d can be determined by the formula d = 3.5(s − 5). Solve for s. Equation Explanation Reason 𝑑 = 3.5(𝑠 − 5) Write original equation. Given 𝑑 = ______________________ Multiply _____________________________________ 𝑑 + _____________ = __________ Add _______________ to each side __________________________ Property of Equality Divide each side by ___________________. __________________________ Property of Equality. Geometry Chapter 2: Reasoning and Proof REFLEXIVE PROPERTY OF EQUALITY Real Numbers Segment Length Angle Measure For any real number a, For any segment AB, For any angle A, SYMMETRIC PROPERTY OF EQUALITY Real Numbers Segment Length Angle Measure For any real numbers, a and b, if a = b, then For any segments AB and CD, if AB = CD, then For any angles A and B, and if 𝒎∠𝑨 = 𝒎∠𝑩 then, TRANSITIVE PROPERTY OF EQUALITY Real Numbers Segment Length Angle Measure For any real numbers a, b, and c, if a = b and b = c, then For any segments AB, CD, and EF if AB = CD, and CD = EF, then For any angles, A, B, and C, if 𝒎∠𝑨 = 𝒎∠𝑩 𝒂𝒏𝒅 𝒎∠𝑩 = 𝒎∠𝑪, then, Geometry Chapter 2: Reasoning and Proof Example 4: Use properties of equality Show that CF = AD.
Statement
Reason
AB = ____________
Given
BC = ____________
Given
AC = AB + BC
______________________________________
DF = ________ + ________
Segment Addition Postulate
DF = BC + AB
________________ Property of Equality
DF = __________
________________ Property of Equality
DF + CD = ________ + CD
________________ Property of Equality
_________ = _________
Substitution Property of Equality
Example 5: Use properties of equality You are designing a logo to sell daffodils. Use the information given.
Determine whether 𝑚∠𝐸𝐵𝐴 = 𝑚∠𝐷𝐵𝐶.
Equation
Reason
𝑚∠1 = ____________
__________________________________
𝑚∠𝐸𝐵𝐴 = ___________________
______________ Addition Postulate
𝑚∠𝐸𝐵𝐴 = ___________________
Substitution Property of Equality
𝑚∠1 + _________ = 𝑚∠𝐷𝐵𝐶
______________ Addition Postulate
𝑚∠𝐸𝐵𝐴 = __________________
________________ Property of Equality
Homework: Pgs. 108 – 109 #’s 3 – 11 ODD, 17 – 25 ODD, 29, 33, 35