Powerpoint Project 5 Adam and Nikki Birnbrey Properties of Equality to Know and Love  Addition Property- If a=b, then a+c= b+c  Subtraction Property-

Slides:



Advertisements
Similar presentations
Chapter 2 Review Lessons 2-1 through 2-6.
Advertisements

2.5 Reasoning in Algebra and Geometry
GOAL 1 COMPARING TYPES OF PROOFS EXAMPLE 1 Vocabulary two-column proof paragraph proof flow proof 3.2 PROOF AND PERPENDICULAR LINES Be sure you identify.
By: James Ryden and Evan Greenberg By: James Ryden and Evan Greenberg By: James Ryden and Evan Greenberg By: James Ryden and Evan Greenberg.
Use right angle congruence
2.5 Reasoning in Algebra and Geometry
4.5 Segment and Angle Proofs
Chapter 2 Review Reasoning and Proof.
Chapter Two Emma Risa Haley Kaitlin. 2.1 Inductive reasoning: find a pattern in specific cases and then write a conjecture Conjecture: unproven statement.
Special Pairs of Angles
Conjectures that lead to Theorems 2.5
Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles.
2-5 Postulates and Paragraph Proofs (p.89)
Reasoning & Proof Chapter 2.
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:
Deductive Reasoning Geometry Chapter 2. Vocabulary Converse-formed by interchanging the hypothesis and the conclusion Statement: If p, then q Converse:
Geometry Trig 2Name______________ Unit 2.2Date _______________ Properties of Algebra Properties of Equality DefinitionExample Addition PropertyIf a = b.
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.
Identify the Property which supports each Conclusion.
Building a System of Geometry Knowledge 2.4
2.4: Building a System of Geometric Knowledge
 Deductive Reasoning is a process of reasoning logically from given facts to a conclusion.  Addition Property of equality if a=b then a+c=b+c  Subtraction.
Some properties from algebra applied to geometry PropertySegmentsAngles Reflexive Symmetric Transitive PQ=QP m
Conjecture: an educated guess
Lesson: 15 – 4 Preparing for Two-Column Proofs
2.6 What you should learn Why you should learn it
Warm Up. Warm Up Answers Theorem and Proof A theorem is a statement or conjecture that has been shown to be true. A theorem is a statement or conjecture.
2.5 Reasoning in Algebra and geometry
Use right angle congruence
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.
DefinitionsTrue / False Postulates and Theorems Lines and Angles Proof.
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:
Intro to Proofs Unit IC Day 2. Do now Solve for x 5x – 18 = 3x + 2.
2.4 Reasoning with Properties from Algebra ?. What are we doing, & Why are we doing this?  In algebra, you did things because you were told to….  In.
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.
2-6 Prove Statements About Segments and Angles Hubarth Geometry.
2.5 Reasoning with Properties from Algebra
2. 6 Prove Statement about Segments and Angles 2
Reasoning in Algebra and Geometry
Reasoning Proof and Chapter 2 If ….., then what?
Reasoning and Proofs Chapter 2.
Do Now Find the value of x that will make a parallel to b. (7x – 8)°
4.5 Segment and Angle Proofs
Chapter 2.6 (Part 1): Prove Statements about Segments and Angles
Y. Davis Geometry Notes Chapter 2.
Use right angle congruence
2.8 Notes: Proving Angle Relationships
CONGRUENCE OF ANGLES THEOREM
Statements About Segments and Angles
2.1 Patterns and Inductive Reasoning
2.5 Reasoning in Algebra and Geometry
2. Definition of congruent segments AB = CD 2.
CONGRUENCE OF ANGLES THEOREM
Vocabulary theorem two-column proof
Prove Statements about Segments and Angles
2.6 Proving Statements about Angles
Put CW/HW on the corner of your desk!
Reasoning and Proofs Deductive Reasoning Conditional Statement
Properties of Equality and Proving Segment & Angle Relationships
Vocabulary theorem two-column proof
Day 5 – Introduction to Proofs
2.6 Proving Statements about Angles
2-6 Prove Statements About Segments and Angles
Bell Work: If you have not turned in your signed syllabus or contract please put it in the basket. Get out your pages from yesterday: 32, 35, On.
2.4 Building a System of Geometry Knowledge
Unit 2: Congruence, Similarity, & Proofs
2.7 Prove Theorems about Lines and Angles
4.5 Segment and Angle Proofs
Presentation transcript:

Powerpoint Project 5 Adam and Nikki Birnbrey

Properties of Equality to Know and Love  Addition Property- If a=b, then a+c= b+c  Subtraction Property- If a=b, then a-c=b-c  Multiplication Property- If a=b, then ac=bc  Division Property- If a=b and c doesn’t = 0 Then a/c= b/c  Substitution Property- If a=b you may replace a with b in any equation containing a in the result

Equivalence Properties of Equality to Know and Love  Reflexive Property- For any real number a, a=a  Symmetric Property- For all real numbers a and b, if a=b, then b=a  Transitive Property- For all real numbers a, b, and c, if a=b and b=c, then a=c

Equivalence Relation To Know And Love = any relation that satisfies these equivalence properties  Reflexive Property- Figure A=Figure A A  Symmetric Property- If Figure A=Figure B, then Figure B=Figure A A  Transitive Property- If Figure A=Figure B and Figure B=Figure C, Then Figure A=Figure C A B C

Overlapping Theorem to Know and Love  Overlapping Segments- Given a segment with points A, B, C, & D arranged as shown the following statements are true: 1. If AB=CD then AC=BD 2. If AC=BD then AB=CD  Overlapping Angles- Given Angle AED with points B and C in its interior as shown, the following statements are true: 1. If Angle AEB=Angle CED then ? 2. If Angle AEC=Angle BED then ? A B C D AB E C D

Vertical Angles Theorem to Know and Love IIf two angles form a pair of vertical angles, then they are congruent. Given: angle 1 and 2 are vertical angles Prove: Angle 1 and 2 are congruent Statements Reasons 1.Angle 1 and 2 are vertical angles 2. Angle 1 + angle 2= 180 Angle 2 + angle 3= Angle 1+ angle 3= angle 2 + angle 3 4.Angle 1= angle 2 (1=2) Given Linear pair property Substitution property of equality Subtraction property of equality

Congruence Supplements Theorem to Know and Love  If two angles are supplements of congruent angles then the two angles are congruent Given: Angle 1=Angle 3, Angle 1 and angle 2 are supplementary, Angle 3 and 4 are supplementary Prove: Angle 2=Angle 4 Statements Reasons 1. <1+<2=180 <3+<4= <1+<2=<3+<4 3. <1=<3 4. <1+<2=<1+<4 5. <2=<4 Definition of Supplementary Angles Transitive Given Substitution Property Subtraction Property 3412

More Theorems to Know and Love  Theorem- Reflection across two parallel lines is equivalent to a translation of twice the distance between the lines and in a direction perpendicular to the lines  Theorem- Reflection across two intersecting lines is equivalent to a rotation about the point of intersection through twice the measure of the angle between the lines

Vocabulary to Know and Love  Equivalence relation= Any relation that satisfies the Reflexive, Symmetric, and Transitive Properties  Inductive reasoning= The process of forming conjectures that are based on observations  Paragraph proof= A form of a proof in which one’s reasoning is explained in paragraph form, as opposed to a two-column proof  Theorem= A statement that has been proved deductively  Two column proof= A proof in which the statements are written in the left-hand column and the reasons are given in the right-hand column  Vertical angles= The opposite angles formed by two intersecting lines

Practice to Know and Love (and a pooton of it) VVertical Angles: Definition, illustrated examples, and an interactive practice quiz

A real pooton of Practice to Know and Love (yeah math )  Given: 15x-5=10x+15 (use properties to prove)  Prove the Overlapping Segments Theorem Given: WX=YZ; Prove WY=XZ W XY Z WX=YZ WX+XY= YZ+XY WX=XY=WY segment additon postulate ______property

….Extra poo  Identify the properties of equality that justify the conclusion. <B= <C; <C= <D  <B= <D ________ AB=CD; CD=AB_______ AB+BC= BC+ CD; AC=BD_______

Finding Values: Problemas (To Know and Love) Find x. 3X- 60 X X 10X