B ELL -R INGER Write the converse of this statement. State whether the statement and its converse are true or false. If both are true, write a biconditional.

Slides:

Advertisements

Similar presentations

Warm Up Identify the hypothesis and conclusion of each conditional; write the converse of the conditional; decide whether the conditional and converse.

Advertisements

2.5 Reasoning in Algebra and Geometry

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

Verifying Segment Relations

3-4 Algebra Properties Used in Geometry The properties of operations of real numbers that you used in arithmetic and algebra can be applied in geometry.

Chapter 2 Properties from Algebra

2.5 Reasoning in Algebra and Geometry

2.4 Reasoning with Properties from Algebra

Section 2.5. Addition PropertyIf a=b, then a+c=b+c If 2=2, then 2+1=2+1 Subtraction PropertyIf a=b, then a-c=b-c If 2=2, then 2-1=2-1 Multiplication PropertyIf.

Chapter Two Emma Risa Haley Kaitlin. 2.1 Inductive reasoning: find a pattern in specific cases and then write a conjecture Conjecture: unproven statement.

Proving Segment Relationships

Unit 2 Part 2 Statement and Reason Proofs. Two Column Proof  Statement | Reason  1 st Statement | Reason  2 nd Statement | Reason  etc…

Lesson 2-4 Reasoning in Algebra. Check Skills You’ll Need 1.Name 1 in two other ways. 2.Name the vertex of 2. 3.If 1 2, name the bisector of AOC. 4.If.

Deductive Reasoning Geometry Chapter 2. Vocabulary Converse-formed by interchanging the hypothesis and the conclusion Statement: If p, then q Converse:

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.

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?

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.

2-2 Properties from Algebra

Properties of Equality and Congruence Section 2.6.

Section 2.4: Reasoning in Algebra

Properties from Algebra

2-2: Properties of Algebra. Properties Page 37: copy into your notes.

Some properties from algebra applied to geometry PropertySegmentsAngles Reflexive Symmetric Transitive PQ=QP m

Conjecture: an educated guess

Reasoning With Properties of Algebra

Section 2-4: Reasoning in Algebra TPI 32A: apply reflective, transitive, or symmetric prooperties of equality or congruence Objectives: Connect reasoning.

Chapter 2 Lesson 4 Objective: To connect reasoning in algebra to geometry.

Geometry 2.5 Big Idea: Reason Using Properties from Algebra.

Goal 1: Use properties from algebra Goal 2: Use properties of length and measure to justify segment and angle relationships CAS 3.

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

They are easier than Geometry ones!!. PROOFS The “GIVEN” is always written first –It is a “GIMME” The “PROVE” should be your last line Make a two column.

Objective: To prove and apply theorems about angles Proving Angles Congruent (2-6)

Reasoning with Properties from Algebra Algebraic Properties of Equality let a, b, and c be real numbers. Addition Property: If a=b, then a+c=b+c. Subtraction.

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 from Algebra (for geometry proof) p. 89 ?

2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,

Chapter 2, Section 1 Conditional Statements. Conditional Statement Also know as an “If-then” statement. If it’s Monday, then I will go to school. Hypothesis:

For numbers 1 & 2 Solve for x and give a reason listed below for each step 1)4m - 8 = -12 2)6r – 3 = -2 ( r + 1 )

Reasoning in Algebra Chapter 2: Reasoning and Proof1 Objectives 1 To connect reasoning in algebra and geometry.

2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

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.

USING PROPERTIES FROM ALGEBRA ALGEBRAIC PROPERTIES OF EQUALITY Let a, b, and c be real numbers. SUBTRACTION PROPERTY ADDITION PROPERTY If a = b, then a.

Lesson 2-2 Properties from Algebra (page 37) Essential Question Can you justify the conclusion of a conditional statement?

Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

Essential Question #1 Why is the use of inductive reasoning important to understanding mathematics?

Reasoning in Algebra & Deductive Reasoning (Review) Chapter 2 Section 5.

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

2-6: Algebraic Proof. Properties Reflexive property – every # equals itself; a=a, 1=1, etc. Symmetric property – You can switch the sides of the equation.

Reasoning in Algebra and Geometry

HMWK: p. 100, #s 17 – 23 odd, 24 – 28 all Game Plan: Warm-up:

2.4 Objective: The student will be able to:

2.4 Reasoning with Properties from Algebra

Objective: To connect reasoning in algebra to geometry.

2.4 Algebraic Reasoning.

2-5 Reason Using Properties from Algebra

Geometry 2.4 Algebra Properties

2.5 Reasoning in Algebra and Geometry

CHAPTER 2: DEDUCTIVE REASONING

Prove Statements about Segments and Angles

Section 2-4: Reasoning in Algebra

Reasoning With Properties of Algebra

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 Reasoning Using Properties from Algebra

2.4 Building a System of Geometry Knowledge

2-6: Algebraic Proof.

2-5 Algebraic Proof Geometry.

Presentation transcript:

B ELL -R INGER Write the converse of this statement. State whether the statement and its converse are true or false. If both are true, write a biconditional statement. IF both are false, write a counterexample. If DE+EF=DF, then points D, E, and F are collinear.

S ECTION 2.2: P ROPERTIES FROM A LGEBRA

P ROPERTIES FROM A LGEBRA Since the lengths of segments and the measure of angles are real numbers, a lot of the properties from algebra can be used in geometry. Here are some important properties from algebra that we will be using.

P ROPERTIES OF E QUALITY Addition Property: If a=b and c=d, then a+c=b+d Subtraction Property: If a=b and c=d, then a-c=b-d Multiplication Property: If a=b, then ca=cb Division Property: If a=b and c≠0, then Substitution Property: If a=b, then either a or b may be substituted for the other in any equation (or inequality)

P ROPERTIES OF E QUALITY C ONT ’ D Reflexive Property of equality or congruence: a=a or and Symmetric Property of equality or congruence : If a=b, then b=a or Ifthen Ifthen Transitive Property of equality or congruence : If a=b and b=c, then a=c If and then Distributive Property: a(b+c)=ab+ac

P ROPERTIES OF C ONGRUENCE Reflexive Property:and Symmetric Property: If then If then Transitive Property: If and then If and then

T RY S OME ! Justify Each statement with a property from algebra or a property of congruence If AB=CD and CD=EF, then AB=EF 3. If RS=TW, then TW=RS 4. If x+5=16, then x=11 5. If 5y=-20, then y=-4 6. If z/5=10, then z= (a+b)=2a+2b 8. If 2z-5=-3, then 2z=2 9. If 2x+y=70 and y=3x, then 2x+3x= If AB=CD, CD=EF and EF=23, then AB=23

S OLVE 3 X =6-1/2 X AND JUSTIFY EACH STEP Steps 1. 3x=6-1/2x 2. 6x=12-x 3. 7x=12 4. X=12/7 Reasons 1. Given 2. Multiplication Property of Equality 3. Addition Property of Equality 4. Division Property of Equality

G IVEN : RT AND PQ ARE INTERSECTING AT S SO THAT RS = PS AND ST = SQ P ROVE : RT = PQ Statements 1. RS=PS; ST=SQ 2. RS+ST=PS+SQ 3. RS+ST=RT; PS+SQ=PQ 4. RT=PQ Reasons 1. Given 2. Addition Prop. Of = 3. Segment Addition Postulate 4. Substitution Prop. R P Q S T

G IVEN : P ROVE : 12 3 O D CB A Statements 1. m<AOC=m<BOD 2. m<AOC=m<1+m<2m <BOD=m<2+m<3 3. m<1+m<2=m<2+m<3 4. m<2=m<2 5. m<1=m<3 Reasons 1. Given 2. Angle Addition Post. 3. Substitution Prop. 4. Reflexive Prop. 5. Subtraction Prop. of =

P RACTICE Do the Proofs Worksheet with a partner or group of 3. Do the Proofs Puzzle Alone!

H OMEWORK : Pg 41 #1-6