2.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Reason Using Properties from Algebra.

Slides:

Advertisements

Similar presentations

1 2-4 Reasoning in Algebra Objectives: Use basic properties of algebra in reasoning Define congruence State the properties of congruence.

Advertisements

Write reasons for each step

Chapter 2 Properties from Algebra

EXAMPLE 4 Use properties of equality LOGO You are designing a logo to sell daffodils. Use the information given. Determine whether m EBA = m DBC. SOLUTION.

Properties from Algebra

4.5 Segment and Angle Proofs

Warm-Up Exercises EXAMPLE 1 Write reasons for each step Solve 2x + 5 = 20 – 3x. Write a reason for each step. Equation ExplanationReason 2x + 5 = 20 –

PROVE STATEMENTS ABOUT SEGMENTS & ANGLES. EXAMPLE 1 Write a two-column proof Write a two-column proof for the situation in Example 4 on page 107. GIVEN:

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Algebraic proof Chapter 2 Section 6.

Warm-up To determine your target heart rate r (in beats per minute) before exercising, use the equation, where a is your age in years. Solve for r. Then.

Algebraic Proofs. Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = t – 7 = 8t (y – 5) – 20 = 0 x = 4 r = 12.2 n = –38 y = 15.

Warm Up Week 7 1) What is the postulate? A B C D m∠ ADB + m ∠ BDC = m ∠ ADC 2) If ∠ 4 and ∠ 5 are a linear pair and ∠ 4 = 79⁰. What is m ∠ 5?

5 Minute Check. 2.5 Reasoning with Properties of Algebra Students will use Algebraic properties in logical arguments. Why? So you can apply a heart rate.

Reasoning with Properties from Algebra. Properties of Equality Addition (Subtraction) Property of Equality If a = b, then: a + c = b + c a – c = b – c.

Section 2.4: Reasoning in Algebra

Chapter 2 Section 4 Reasoning in Algebra. Properties of Equality Addition Property of Equality If, then. Example: ADD 5 to both sides! Subtraction Property.

2.4 Algebraic Reasoning. What We Will Learn O Use algebraic properties of equality to justify steps in solving O Use distributive property to justify.

2.4 Reasoning with Properties of Algebra Mrs. Spitz Geometry September 2004.

Holt Geometry 2-5 Algebraic Proof 2-5 Algebraic Proof Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Reasoning With Properties of Algebra

Warm-Up Exercises EXAMPLE 1 Write reasons for each step Solve 2x + 5 = 20 – 3x. Write a reason for each step. Equation ExplanationReason 2x + 5 = 20 –

Geometry 2.5 Big Idea: Reason Using Properties from Algebra.

Chapter 2.5 Notes: Reason Using Properties from Algebra Goal: You will use algebraic properties in logical arguments.

2.3 Diagrams and 2.4 Algebraic Reasoning. You will hand this in P. 88, 23.

2-5 Reasoning with Properties from Algebraic Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Unit 2 Solve Equations and Systems of Equations

2.5 Reason Using Properties from Algebra Objective: To use algebraic properties in logical arguments.

Reasoning with Properties from Algebra Chapter 2.6 Run Warmup.

Reasoning with Properties from Algebra. Properties of Equality For all properties, a, b, & c are real #s. Addition property of equality- if a=b, then.

2.4 Reasoning with Properties of Algebra Mr. Davenport Geometry Fall 2009.

Warm Up Lesson Presentation Lesson Quiz

2-5 Reason Using Properties from Algebra Hubarth Geometry.

2.5 Algebra Reasoning. Addition Property: if a=b, then a+c = b+c Addition Property: if a=b, then a+c = b+c Subtraction Property: if a=b, then a-c = b-c.

11/22/2016 Geometry 1 Section 2.4: Reasoning with Properties from Algebra.

Write a two-column proof

Warm Up Rewrite each term using math symbols you learned in chapter 1 (symbols for a line, angle, ray, etc.) Example: MN Ray MN _________________________________________________________.

2.4 Objective: The student will be able to:

2.5 and 2.6 Properties of Equality and Congruence

Reasoning Proof and Chapter 2 If ….., then what?

Objectives Students will…

4.5 Segment and Angle Proofs

2.4 Algebraic Reasoning.

2-5 Reason Using Properties from Algebra

Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Section 2-4: Reasoning in Algebra

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Reasoning With Properties of Algebra

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2.5 Reason Using Properties from Algebra

Chapter 2.5 Reasoning in Algebra and Geometry

2.4 Reasoning with Properties of Algebra

Warm Up Determine whether each statement is true or false. If false, give a counterexample. 1. It two angles are complementary, then they are not congruent.

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Algebraic proofs A proof is an argument that uses logic to show that a conclusion is true. Every time you solved an equation in Algebra you were performing.

Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = 8.7

2.5 Reasoning Using Properties from Algebra

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = 8.7

2-6 Prove Statements About Segments and Angles

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

4.5 Segment and Angle Proofs

Objective SWBAT use the properties of equality to write algebraic proofs. HW Page 107 {3-15 odd, 23, 25, 31}

Warm Up Solve each equation. 1. 3x + 5 = r – 3.5 = 8.7

2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz

Presentation transcript:

2.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Reason Using Properties from Algebra

2.5 Warm-Up 1.6x + 2 = –3x – 16 2.–4(x – 8) = –16 ANSWER 12 Solve each equation. ANSWER –2 3. Solve P = 2l + 2w for w. ANSWER W = P – 2 l 2

2.5 Warm-Up ANSWER 52º; m S = m T 4. S is the complement of R. If m R = 38º, find m S. If T is also the complement of R, what is true about m S and m T?

2.5 Example 1 Solve 2x + 5 = 20 – 3x. Write a reason for each step. Given Addition Property of Equality Simplify. Subtraction Property of Equality Equation ExplanationReason 2x + 5 = 20 – 3x Write original equation. 2x x = 20 – 3x + 3x Add 3x to each side. 5x + 5 = 20 Combine like terms. 5x = 15 Subtract 5 from each side. x = 3 Divide each side by 5. Division Property of Equality The value of x is 3.ANSWER

2.5 Example 2 Solve –4(11x + 2) = 80. Write a reason for each step. SOLUTION EquationExplanationReason –4(11x + 2) = 80 Write original equation. Given –44x – 8 = 80 Multiply. Distributive Property –44x = 88 Add 8 to each side. Addition Property of Equality x = –2 Divide each side by –44. Division Property of Equality

2.5 Example 3 When you exercise, your target heart rate should be between 50% to 70% of your maximum heart rate. Your target heart rate r at 70% can be determined by the formula r = 0.70(220 – a) where a represents your age in years. Solve the formula for a. Heart Rate SOLUTION Equation ExplanationReason r = 0.70(220 – a) Write original equation. Given r = 154 – 0.70a Multiply. Distributive Property

2.5 Example 3 Equation ExplanationReason r – 154 = –0.70a Subtract 154 from each side. Subtraction Property of Equality –0.70 r – 154 = a Divide each side by –0.70. Division Property of Equality

2.5 Guided Practice Solve the equation and write a reason for each step. 1. 4x + 9 = –3x + 2 Equation ExplanationReason 4x + 9 = –3x + 2 Write original equation. Given 7x + 9 = 2 Add 3x to each side. Addition Property of Equality Subtract 9 from each side. Subtraction Property of Equality x = –1 Divide each side by 7. Division Property of Equality 7x = –7 ANSWER

2.5 Guided Practice Solve the equation and write a reason for each step x + 3(7 – x) = –1 Divide each side by x + 3(7 – x) = –1 Write original equation. Given 14x +21 – 3x = –1 Multiply. Distributive Property 11x = –22 Subtract 21 from each side. Subtraction Property of Equality x = –2 Division Property of Equality 11x +21= –1 Simplify Simplify. Equation ExplanationReason ANSWER

2.5 Guided Practice 3. Solve the formula A = bh for b. 1 2 Formula ExplanationReason Write original equation. Given A = 1 2 bh Multiply Multiplication property Divide Division property 2A = bh 2A = b h ANSWER

2.5 Example 4 You are designing a logo to sell daffodils. Use the information given. Determine whether m EBA = m DBC. LOGO SOLUTION Equation ExplanationReason m 1 = m 3 Marked in diagram. Given m EBA = m 3+ m 2 Add measures of adjacent angles. Angle Addition Postulate m EBA = m 1+ m 2 Substitute m 1 for m 3. Substitution Property of Equality

2.5 Example 4 m 1 + m 2 = m DBC Add measures of adjacent angles. Angle Addition Postulate m EBA = m DBC Transitive Property of Equality Both measures are equal to the sum of m 1 + m 2. Equation ExplanationReason

2.5 Example 5 In the diagram, AB = CD. Show that AC = BD. SOLUTION Equation ExplanationReason AB = CD Marked in diagram. Given AC = AB + BC Add lengths of adjacent segments. Segment Addition Postulate BD = BC + CD Add lengths of adjacent segments. Segment Addition Postulate

2.5 Example 5 Equation ExplanationReason AB + BC = CD + BC Add BC to each side of AB = CD. Addition Property of Equality AC = BD Substitute AC for AB + BC and BD for BC + CD. Substitution Property of Equality

2.5 Guided Practice Name the property of equality the statement illustrates. Symmetric Property of EqualityANSWER 5. If JK = KL and KL = 12, then JK = 12. ANSWERTransitive Property of Equality 4. If m 6 = m 7, then m 7 = m m W = m W ANSWER Reflexive Property of Equality

2.5 Lesson Quiz Solve. Give a reason for each step. 1. –5x + 18 = 3x – 38 ANSWER Equation (Reason) –5x + 183x – 38 = (Given) –8x + 18 = –38 (Subtr. Prop. Of Eq.) = –8x–56 (Subtr. Prop. Of Eq.) = x 7 (Division Prop. Of Eq.)

2.5 Lesson Quiz Solve. Give a reason for each step. 2. –3(x – 5) = 2(x + 10) ANSWER Equation (Reason) –3(x – 5)2(x + 10) = (Given) = 155x +20 (Addition Prop. Of Eq.) x (Division Prop. Of Eq.) –1 = = 5x5x (Subtr. Prop. Of Eq.) –5 –3x + 15 = 2x + 20 (Distributive Prop.)

2.5 Lesson Quiz ANSWERTransitive Property Of Equality 4. If CD = EF, then EF = CD. Symmetric Property Of EqualityANSWER 3. If m 3 = m 5 and m 5 = m 8, then m 3 = m 8.