Geometric Proofs Standards 2i & 2j.

Slides:

Advertisements

Similar presentations

Advertisements

Sec 2-6 Concept: Proving statements about segments and angles Objective: Given a statement, prove it as measured by a s.g.

Lesson 2.5 AIM: Proving Angles Congruent

Lesson 2.4 AIM: Properties of Equality and Congruence DO NOW: Draw a conclusion from the following statements. 1. If an integer ends in 4, it is divisible.

Proving Angles Congruent

SWLT: Write proofs using geometric theorems and use properties of special pairs of angles.

3.3 Parallel and Perpendicular Lines To Relate Parallel and Perpendicular Lines.

Use right angle congruence

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.

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

Proving Angle Relationships

ANGLE PAIR PROOFS Let the fun begin  Pick Up Notes from back  Get HW out to grade.

Proving angles congruent. To prove a theorem, a “Given” list shows you what you know from the hypothesis of the theorem. You will prove the conclusion.

Proving Triangles Congruent STUDENTS WILL BE ABLE TO… PROVE TRIANGLES CONGRUENT WITH A TWO COLUMN PROOF USE CPCTC TO DRAW CONCLUSIONS ABOUT CONGRUENT TRIANGLES.

Vocabulary algebraic proof – Made up of algebraic statements two-column proof/formal proof – contains statements and reasons in two columns.

Warm Up Complete each sentence.

3.3 – Proves Lines are Parallel

Lesson: 15 – 4 Preparing for Two-Column Proofs

2.6 What you should learn Why you should learn it

Chapter 2: Reasoning and Proof Prove Angle Pair Relationships.

4-7 Vertical Angles. Vertical angle definition Two angles are vertical angles if their sides form two pairs of opposite rays.  1 and  2 are vertical.

Lesson 2.7 Transitive and Substitution Properties Objective: After studying this lesson you will be able to apply the transitive properties of segments.

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

Isosceles Triangle Theorem (Base Angles Theorem)

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

Warm Up Week 8 If it does not snow, then we will go camping. If we go camping then we will cook marshmallows. The following statement depicts.

2.6 Proving Statements about Angles Mrs. Spitz GeometryFall 2004.

StatementsReasons 1. ________________________________ 2.  1   2 3. ________________________________ 4. ________________________________ 1. ______________________________.

CAMPBELL COUNTY HIGH SCHOOL Chapter 2: Properties Review.

+ DO NOW- Complete #1-5 on the proofs worksheet that you picked up from the back of the classroom.

ADVANCED GEOMETRY SECTION 2.7 Transitive and Substitution Properties.

Puzzle Given:  1 and  5 are supplementary.  3 and  5 are supplementary. Prove: m  1 = m  3 Statements Reasons Q P R ST U Given.

Congruent Angles.

Corresponding Angles Postulate

Warm up Draw two congruent angles: Draw two adjacent angles:

Chapter 2.6 Algebraic Proof.

Chapter 2.6 (Part 1): Prove Statements about Segments and Angles

Use right angle congruence

Give a reason for each statement.

Two Column Proofs Angles

Use right angle congruence

2.8 Notes: Proving Angle Relationships

CONGRUENCE OF ANGLES THEOREM

Unit 1 Day 10 TWO COLUMN PROOFS.

If tomorrow is Thursday, then today is Wednesday.

The Addition Postulates and some important definitions, Module 1

2. Definition of congruent segments AB = CD 2.

CONGRUENCE OF ANGLES THEOREM

Agenda EQ: How do we write 2-column Geometric Proofs? Agenda

2.6 Proving Statements about Angles

Mathematical Justifications

2.6 Proving Statements about Angles

Proving things about Angles

Congruence and Triangles

Proving Statements About Angles

3.3 Proofs with parallel lines

Day 5 – Introduction to Proofs

2.6 Proving Statements about Angles

2-6 Proving Angles Congruent

This is a postulate, not a theorem

Proving things about Angles

Give a reason for each statement.

Proving Statements about Angles

Unit 2: Congruence, Similarity, & Proofs

2.7 Prove Theorems about Lines and Angles

Presentation transcript:

Geometric Proofs Standards 2i & 2j

Given: and are supplementary Prove: and are supplementary and are supplementary Given and are supplementary Definition of Supplementary Angles Transitive Property

Transitive Property If and then The b’s are what make it transitive

Given: and are supplementary Prove: and are supplementary and are supplementary Given and are supplementary Definition of Supplementary Angles Transitive Property Reflexive Property of Eq. Addition/Subtraction Property Definition of Congruent Angles

Given: and are right angles Prove: and are right angles Given Definition of Right Angles Transitive (or Substitution) Definition of Congruent Angles