Proving Angle Relationships

Slides:

Advertisements

Similar presentations

2.6 Proving Angles Congruent

Advertisements

Lesson 2 – 8 Proving Angle Relationships

Bell Work 1) Solve for each variable 2) Solve for each variable 3 and 4) Transitive Property of equality Definition of Congruence Given Definition of Congruence.

2-8: Proving Angle Relationships

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

2.6 Proving Statements about Angles Mrs. Spitz GeometryFall 2004.

2.6 Proving Statements about Angles

Warm Up Given: ∠ 1 ≅ ∠ 2 m ∠ 2 = 60° m ∠ 3 = 60° Prove: ∠ 1 ≅ ∠

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

Angle Pair Relationships

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.

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.

Name that property Use your white board and write down your response. Hold it up When I see all boards I will tell you the correct response.

2.7 Prove Angle Pair Relationships

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.

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

Three Types of Special Angles

Proving lines parallel Chapter 3 Section 5. converse corresponding angles postulate If two lines are cut by a transversal so that corresponding angles.

2.6 What you should learn Why you should learn it

Chapter 2: Reasoning and Proof Prove Angle Pair Relationships.

Chapter 3 Vocabulary BINGO. Add these terms to your card, in no particular order… Vertical Angles Theorem Corresponding Angles Postulate Alternate Interior.

2.6 Proving Statement about Angles

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,

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

EXAMPLE 3 Prove the Vertical Angles Congruence Theorem

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.

2.8 Proving Angle Relationships What you’ll learn: 1.To write proofs involving supplementary and complementary angles. 2.To write proofs involving congruent.

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.

Section 1.6 Angle Pair Relationships standard #13 7/3/2016.

Congruent Angles.

2.6 Proving Geometric Relationships

Chapter 1 section 7 Angle relationships

Section 2.8: Proving Angle Relationships

Give a reason for each statement.

Describe Angle Pair Relationships

2.8 Notes: Proving Angle Relationships

Chapter 1: Essentials of Geometry

CONGRUENCE OF ANGLES THEOREM

Statements About Segments and Angles

CONGRUENCE OF ANGLES THEOREM

Types of Angles & Their Relationships

Describe Angle Pair Relationships

2.6 Proving Statements about Angles

Mathematical Justifications

2.6 Proving Statements about Angles

Angle Pair Relationships

Proving things about Angles

Proving Statements About Angles

Angle Pair Relationships

Properties of Equality and Proving Segment & Angle Relationships

2.6 Proving Statements about Angles

2.7 Prove ∡ Pair Relationships

Special Pairs of Angles

2-6 Proving Angles Congruent

Proving things about Angles

2.6 Deductive Reasoning GEOMETRY.

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

Proving Statements about Angles

Unit 2: Congruence, Similarity, & Proofs

2.7 Prove Theorems about Lines and Angles

Proving Angle Pair Relationships

Presentation transcript:

Proving Angle Relationships Chapter 2 Section 8

Angle Addition Postulate

Using the Angle Addition Postulate 1 EXAMPLE Using the Angle Addition Postulate 75

Find the measure of each numbered angle and name the theorem that justifies your work. They are a linear pair, so they will add to 180. Solve for x. All angles add to 180. Solve for x. Angles 1 and 2 add to 90. Angles 11 and 13 add to 180.

Properties of Congruent Angles Reflexive Property ∠ A ≅ ∠ A Symmetric Property If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A Transitive Property If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C

Theorem 2.4:Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.

Theorem 2.5:Congruent Complements Theorem If two angles are complementary to the same angle (or to congruent angles), then they are congruent.

Theorem 2.8 Vertical Angles Theorem Vertical angles are congruent. 2 3 1 4 ∠1 ≅ ∠3; ∠2 ≅ ∠4

Example – Using Vertical Angles Theorem Find the value of x 4x 3x + 35 What is each angle measure? Set 4x = 3x + 35 Solve for x

Right Angle Theorems

More right angle theorems

Have a great day! 