Goal: The learner will use properties of special pairs of angles.

Slides:

Advertisements

Similar presentations

2.6 Proving Angles Congruent

Advertisements

Lesson 2 – 8 Proving Angle Relationships

2-8: Proving Angle Relationships

More Angle Relationships. Deductive Reasoning To deduce means to reason from known facts When you prove a theorem, you are using deductive reasoning using.

2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.

Ch 1.6 Standard 13.0: Students prove relationships between angles by using properties of complementary, supplementary, and vertical angles. Objective:

2.6 Proving Statements about Angles

2.6 Proving Statements about Angles Geometry. Standards/Objectives Students will learn and apply geometric concepts. Objectives: Use angle congruence.

Proving Angle Relationships Section 2-8. Protractor Postulate Given and a number r between 0 and 180, there is exactly one ray with endpoint A, extending.

Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles.

Chapter 2.7 Notes: Prove Angle Pair Relationships

Chapter 2.7 Notes: Prove Angle Pair Relationships Goal: You will use properties of special pairs of angles.

Proving Angle Relationships

2.6 Proving Statements about Angles. Properties of Angle Congruence ReflexiveFor any angle, A

Geometry Section 1.6 Special Angle Pairs. Two angles are adjacent angles if Two angles are vertical angles if.

2.7 Prove Angle Pair Relationships

2-8 Proving Angle Relationships day 2

Prove Theorems Advanced Geometry Deductive Reasoning Lesson 4.

P. 114: 23 – 28. Given Transitive prop. congruence Definition of congruence Given Transitive prop. Equality/Substitution.

2-4 Special Pairs of Angles Objectives -Supplementary Angles Complementary Angles -Vertical angles.

Three Types of Special Angles

PROVING LINES PARALLEL. CONVERSE OF  … Corresponding Angles Postulate: If the pairs of corresponding angles are congruent, then the lines are parallel.

2.6 What you should learn Why you should learn it

Chapter 2: Reasoning and Proof Prove Angle Pair Relationships.

Unit 01 – Lesson 13 – Proving Angle Relationships ESSENTIAL QUESTION How can you prove a mathematical statement? Scholars will… Write proofs involving.

Ch. 2.6: Proving Statements about Angles

Proving Angles Congruent Chapter 2 Section 6. Theorem A conjecture or statement that you can prove true. You can use given information, definitions, properties,

3.2 Proof and Perpendicular Lines

All right angles are congruent BCD A TheoremGivenStatementReason If 2 angles are complements of the same angle, then they are congruent Complements of.

Angle Relationship Proofs. Linear Pair Postulate  Angles which form linear pairs are supplementary.

Thursday, August 30, 2012 Homework: p Complete #15-26 mentally; complete #27-31 odd, 34 & 35 in writing.

2.4: Special Pairs of Angles

Chapter Two: Reasoning and Proof Section 2-5: Proving Angles Congruent.

EXAMPLE 3 Prove the Vertical Angles Congruence Theorem

2/17/ : Verifying Angle Relationships 1 Expectation: You will write proofs in “If, then…” form.

Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Objective:Prove Angle Pair Relationships Prove Theorems- use properties, postulates, definitions and other proven theorems Prove: Right Angles Congruence.

2.6 Proving Statements about Angles Mrs. Spitz GeometryFall 2004.

2-4 Special Pairs of Angles. A) Terms 1) Complementary angles – a) Two angles whose sum is 90° b) The angles do not have to be adjacent. c) Each angle.

Congruent Angles.

2.6 Proving Geometric Relationships

Proving Lines Parallel

Chapter 2 Reasoning and Proof.

Section 2.8: Proving Angle Relationships

Give a reason for each statement.

Lesson 14.1: Angles Formed by Intersecting Lines

2.8 Notes: Proving Angle Relationships

CONGRUENCE OF ANGLES THEOREM

Statements About Segments and Angles

2.8 Proving Angle Relationships

CONGRUENCE OF ANGLES THEOREM

Types of Angles & Their Relationships

Describe Angle Pair Relationships

2.6 Proving Statements about Angles

2.6 Proving Statements about Angles

Proving things about Angles

2.6 Proving Statements about Angles

2.7 Prove ∡ Pair Relationships

Special Pairs of Angles

This is a postulate, not a theorem

Proving things about Angles

Lesson 1-5 Pairs of Angles.

2.6 Deductive Reasoning GEOMETRY.

Proving Statements about Angles

Unit 2: Congruence, Similarity, & Proofs

2.7 Prove Theorems about Lines and Angles

Proving Angle Pair Relationships

Chapter 2 Reasoning and Proof.

Presentation transcript:

Goal: The learner will use properties of special pairs of angles. Lesson 2.7 Prove Angle Pair Relationships

Vocabulary Review Complementary Angles Supplementary Angles Linear Pair Vertical Angles

Right Angles Congruence Theorem All right angles are congruent. Let’s Prove It!

Given: Prove: 1 2

C D B A

Congruent Supplements Theorem If two angles are supplementary to the same angle, then they are congruent. 1 2 3

Would the same idea apply to complementary angles? Congruent complements Theorem: If two angles are complementary to the same angle, then they are congruent.

Linear Pair Postulate: If two angles form a linear pair, then they are supplementary. Is the converse true?

Vertical Angles Theorem: vertical angles are congruent. 2 3 1 4

Application of the Vertical Angles Theorem

Application of the Vertical Angles Theorem Only with Algebra Find y and the measure of the angle. 7y 3x-21 2x + 4 5y+36 Find the value of x.

Find x and the measure of the two angles.

Getting Closure What is the relationship between: Vertical Angles Supplementary Angles Complementary Angles Linear Pair