Welcome back…hope you had a wonderful break! Bellringer…Monday (Everyone: new sheet of GRAPH paper, label with name, date) Graph the line segment & find.

Slides:

Advertisements

Similar presentations

Inverses, Contrapositives, and Indirect Reasoning

Advertisements

Inverses, Contrapositives, and Indirect Reasoning

Conditional Statements

Chapter 2 Geometric Reasoning

Write the negation of “ABCD is not a convex polygon.”

TRIANGLE SUM PROPERTIES 4.1. TO CLARIFY******* A triangle is a polygon with three sides. A triangle with vertices A, B, and C is called triangle ABC.

CONFIDENTIAL 1 Geometry Proving Lines Parallel. CONFIDENTIAL 2 Warm Up Identify each of the following: 1) One pair of parallel segments 2) One pair of.

GEOMETRY REVIEW Look how far we have come already!

2.1 Conditional Statements Note, there will be a notes handout for 2.1 given in class.

Directions: Scroll through the presentation and enter the answers (which are really the questions) and the questions (which are really the answers).

10/21/2015Geometry1 Section 2.1 Conditional Statements.

2.1 Conditional Statements. Conditional Statement  Conditional statement has two parts, hypothesis and a conclusion.  If _____________, then____________.

Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4.

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.

Verifying Angle Relations. Write the reason for each statement. 1) If AB is congruent to CD, then AB = CD Definition of congruent segments 2) If GH =

Conditional Statements

Chapter 1 Introduction to Geometry. Slide Getting Started Points – To name a point always use Lines – All lines are and extend in both directions.

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the.

Section 2.2 Conditional Statements 1 Goals Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional.

Conjecture: an educated guess

Inductive and Deductive Reasoning. Notecard 30 Definition: Conjecture: an unproven statement that is based on observations or given information.

2.2.1 Analyze Conditional Statements and Proof Chapter 2: Reasoning and Proof.

CONGRUENCE OF ANGLES THEOREM

Conditional Statements Geometry Chapter 2, Section 1.

Inductive and Deductive Reasoning. Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts:

Geometry Review 1 st Quarter Definitions Theorems Parts of Proofs Parts of Proofs.

Warm Up: Identify the property that justifies each statement.

Section Proving Statements about Angles.

Geometry - Unit 3 $100 Parallel Lines Polygons Equations of Lines Proofs $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200.

The answers to the review are below. Alternate Exterior Angles Postulate Linear Pair Theorem BiconditionalConclusion Corresponding Angles Postulate 4 Supplementary.

DefinitionsTrue / False Postulates and Theorems Lines and Angles Proof.

Using Special Quadrilaterals

Unit 2: Reasoning and Proof

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:

Solve for x and y: 43° 75° y° x° 75° = y + 43° 75 – 43 = y 32° = y z° x and 43° are Alternate Interior Angles 43° = x.

Inductive Reasoning & Conjecture What is a Conjecture? What is inductive reasoning?

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.

Essential Question #1 Why is the use of inductive reasoning important to understanding mathematics?

2-6 Proving Statements about Angles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Conditional Statements

2.2 – Analyze Conditional Statements

Section 2.1 Conditional Statements

Corresponding Angles Postulate

Reasoning Proof and Chapter 2 If ….., then what?

Contrapositive, Inverse, and Converse

Reasoning and Proofs Chapter 2.

Chapter 2 Review Geometric Reasoning.

Chapter 2 Quiz Review.

Do Now Find the value of x that will make a parallel to b. (7x – 8)°

Geometry Ch. 2 Review Created by Educational Technology Network

Two Column Proofs Angles

Prove Angle Pair Relationships

Angle Pairs More Angle Pairs Definitions Pictures Angles

2-2 Conditional Statements

Test corrections Need to write each problem you missed. Including the incorrect answer. Show ALL work!! If you just put the correct letter you will not.

2.6 Proving Statements about Angles

2.1 Conditional Statements

Proving Statements About Angles

Reasoning and Proofs Deductive Reasoning Conditional Statement

Chapter 2.2 Notes: Analyze Conditional Statements

This is a postulate, not a theorem

Converse Definition The statement obtained by reversing the hypothesis and conclusion of a conditional.

Section 1.7 The Formal Proof of a Theorem

Warm Up 2-23. In a conditional statement, the “if” portion of the statement is called the hypothesis, and the “then” portion is called the conclusion.

Bellringer Work on Wednesday warm up.

Unit 2: Congruence, Similarity, & Proofs

2.7 Prove Theorems about Lines and Angles

Chapter 2 Reasoning and Proof.

Presentation transcript:

Welcome back…hope you had a wonderful break! Bellringer…Monday (Everyone: new sheet of GRAPH paper, label with name, date) Graph the line segment & find its length: T (4, -3) H (-5, 2)

Properties of Equality

Properties of Equality ( ) or Congruence ( )

Definition of congruent angles

Definition of Right Angles:

Prove it! Statements:Reasons: 1. <A is a right angle <B is a right angle m<A = 90° Definition of right angle Substitution. 6.<A < B6. Definition of congruent angles.

If <A and <B are supplementary and < B and < C are congruent. Prove that m<A + m<C=180*. StatementsReasons 1.<A & <B are supplementary1. Given 2.<B & <C are congruent2. Given 3.m<A + m<B =180*3. Def. of supplementary angles 4.m<B = m<C4. Def. of congruent angles 5.m<A + m<C = 180*5. Substitution

Jumbled Proofs Packet Get them in order: Write in correct order (same or different page) Cut & paste in correct order on another page

COW Day….math XL #4 (proofs)

Bellringer…Tuesday COPY the following and DRAW a picture showing the points are collinear: Given: H, I, J, and K are collinear points HJ = IK Prove: HI = JK and that the same segments are congruent.

Conditional Statements A statement with two parts: hypothesis and conclusion IF… THEN…

If you vote in the election, then ____________________. (let’s just name one option here, not all requirements)

Converse Switch (transpose) the hypothesis and conclusion.

Inverse Negate (____________) the hypothesis and conclusion of a conditional statement ***Use the original statement here!***

Contrapositive Negate both the hypothesis and conclusion of the converse ***Inverse of the converse***

If it is snowing, then it is cold.

Which is true??? Converse: If it is cold, then it is snowing. Inverse: If it is not snowing, then it is not cold. Contrapositive: If it is not cold, then it is not snowing.

Write the three other statements for the statements below. Then tell whether each statement is true (T) or false (F). 1.If a polygon is a triangle, then the sum of the measures of its interior angles is 180*. 2.If you drive a car, then you are at least 16 years old. 3.If two angles are vertical angles, then they are congruent.