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

Slides:



Advertisements
Similar presentations
September 8, 2011 "The way to be nothing is to do nothing." -- Nathaniel Howe Test prep, p. 18 #
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.
Reflexive example: AB = AB Symmetric example: AB = BA
Bellringer.
Verifying Segment Relations
2.6 Prove Statements About Segments and Angles
Use right angle congruence
Warm Up Solve each equation t – 7 = 8t (y – 5) – 20 = 0 x = 7 r = 12.2 or n = 17 y = 15.
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
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:
Algebraic proof Chapter 2 Section 6.
Honors Geometry Intro. to Deductive Reasoning. Reasoning based on observing patterns, as we did in the first section of Unit I, is called inductive reasoning.
Identify the Property which supports each Conclusion.
Building a System of Geometry Knowledge 2.4
 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.
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
Vocabulary algebraic proof – Made up of algebraic statements two-column proof/formal proof – contains statements and reasons in two columns.
Section 2.4: Reasoning in Algebra
Chapter 2 Section 5. Objective  Students will make a connection between reasoning in Algebra and reasoning in Geometry.
1. If p  q is the conditional, then its converse is ?. a. q  pb. ~q  pc. ~q  ~pd. q  ~p 2. Which statement is always true? a. x = xb. x = 2c. x =
Chapter 2 Section 4 Reasoning in Algebra. Properties of Equality Addition Property of Equality If, then. Example: ADD 5 to both sides! Subtraction Property.
Reasoning With Properties of Algebra
Lesson 2 – 6 Algebraic Proof
Proofs!!! Ok just little ones :).
2.3 Diagrams and 2.4 Algebraic Reasoning. You will hand this in P. 88, 23.
1.6. DEFINITIONS  An equation is a statement that two expressions are equal.  Usually contains 1 or more variables  A variable is a symbol that represents.
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.
GEOMETRY CHAPTER 2 Deductive Reasoning pages
Proofs!!! Ok just little ones :) Properties of Equality Addition Property –If a = b, then a + c = b + c Subtraction Property –If a = b, then a - c =
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.
Chapter 2: Reasoning & Proof 2.4 Reasoning in Algebra.
Given an equation, you can … * Add the same value (or equivalent values) to both sides, If a = b, then a + 7 = b + 7 * Subtract the same value (or equivalent.
2.6 Algebraic Proof. Objectives Use algebra to write two-column proofs Use algebra to write two-column proofs Use properties of equality in geometry proofs.
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,
Intro to Proofs Unit IC Day 2. Do now Solve for x 5x – 18 = 3x + 2.
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.
Ch 2-5 Reasoning in Geometry and Algebra
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.
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)
2-6 Prove Statements About Segments and Angles Hubarth Geometry.
Algebraic Proofs. 1. Transitive property of equality 2. Symmetric property of equality 3. Reflexive property of equality 4. Substitution 5. Addition property.
Reasoning in Algebra and Geometry
2.5 and 2.6 Properties of Equality and Congruence
Proving Statements about Segments
Chapter 2.6 (Part 1): Prove Statements about Segments and Angles
2.5 Reasoning with properties from Algebra
2.5 – Reasoning Using Properties of Algebra
2.4 Algebraic Reasoning.
Use right angle congruence
Unit 1 Day 10 TWO COLUMN PROOFS.
2.5 Reasoning in Algebra and Geometry
2. Definition of congruent segments AB = CD 2.
Proofs.
Prove Statements about Segments and Angles
Reasoning With Properties of Algebra
2.6 Proving Statements about Angles
DO NOW.
Day 5 – Introduction to Proofs
Properties of Equality
Last Night’s Homework: 2.2 Handout Tonight’s Homework: 2.3 Handout
2.7 Proving Segment Relationships
2-6 Prove Statements About Segments and Angles
Homework Pg107(2,6,10,12-15,25-28,30-32,49).
Verifying Segment Relationships
Presentation transcript:

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

Properties of Equality and Congruence A. Addition Property If a = b, then a + c = b + c B. Subtraction Property If a = b, then a c = b c C. Multiplication Property If a = b, then a*c = b*c D. Division Property If a = b, and c ≠ 0, then a/c = b/c E. Reflexive Property of Equality a = a F. Symmetric Property of Equality If a = b, then b = a G. Transitive Property of Equality If a = b and b = c, then a = c H. Substitution Property If a = b, then b can replace a in any Expression I. Distributive Property a(b + c) = ab + ac a(b c) = ab ac J. Reflexive Property of Congruence ∠ A ≅ ∠ A K. Symmetric Property of Congruence If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A L. Transitive Property of Congruence If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C

First…. Theorem : a conjecture or statement that you prove true.

Remember…

W.S. Proof 2