2.2 Definitions and Biconditional Statements. Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular.

Slides:

Advertisements

Similar presentations

DO NOW Key Words in Geometry With a neighbor, discuss the difference between the key location words in geometry in relation to Points, Lines and Planes.

Advertisements

If-Then Statements 2-1.

Biconditionals & Counterexamples Geometry Chapter 02 A BowerPoint Presentation.

Bell Work 1) Write the statement in “If/Then” Form. Then write the inverse, converse, and contrapositive: a) A linear pair of angles is supplementary.

Notes on Logic Continued

Conditional Statements

Unit 3 Lesson 2.2: Biconditionals

2.2 Analyzing Conditional Statements. Conditional Statements: Conditional Statement (In “If-Then” form): “If it is a bird, then it has feathers.” Ex.

Theorems Relating Lines and Planes

Honors Geometry.  How many lines can be passed through one point?  How many planes can be passed through one point?  How many planes can be passed.

2.4 Use Postulates and Diagrams You will use postulates involving points, lines, and planes. Essential Question: How can you identify postulates illustrated.

Analyzing Conditional Statements A _______________________________ is a logical statement that has two parts, a hypothesis and a conclusion.

2.1 Conditional Statements Goals Recognize a conditional statement Write postulates about points, lines and planes.

Biconditionals & Definitions. Biconditional Statement Contains the phrase “if & only if” Abbr. iff It is a conditional statement & its converse all in.

2.2 Definition and Biconditional Statements Use definitions and biconditional statements.

Do Now Each of the letters stands for a different digit. The first digit in a number is never zero. Replace the letters so that each sum is correct.

Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement.

2.2 Write Definitions as Conditional Statements

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

Unit 2 Part 1 Conditional, Converse, Inverse, and Contra- Positive Statements.

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

Chapter 2.2 Notes: Analyze Conditional Statements Goal: You will write definitions as conditional statements.

Chapter 2 Section 2 Biconditionals and Definitions.

2.2 Definitions and Biconditional Statements

Warm Up Week 6 1) State the postulate that shows the statement to be false: A line contains at least three points.

EXAMPLE 1 Rewrite a statement in if-then form

Unit 2 Reasoning and Proof “One meets his destiny often in the road he takes to avoid it.” ~ French Proverb.

Section 2-2: Biconditionals and Definitions. Conditional: If two angles have the same measure, then the angles are congruent. Converse: If two angles.

Chapter 2: Reasoning & Proof 2.2 Biconditionals & Definitions.

 When a conditional and its converse are both true, we combine them to make a biconditional.  Example:  Biconditional – An angle is right if and only.

B ICONDITIONALS AND DEFINITIONS BIG IDEA: REASONING AND PROOF ESSENTIAL UNDERSTANDINGS: A definition is good if it can be written as a biconditional. Every.

2.3 Biconditionals and Definitions 10/8/12 A biconditional is a single true statement that combines a true conditional and its true converse. You can join.

Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

2-3 Biconditionals and Defintions. Biconditional- a statement that is the combination of a conditional statement and its converse. If the truth value.

Warm-Up Exercises GUIDED PRACTICE for Example 1 Rewrite the conditional statement in if-then form. 1. All 90 ° angles are right angles. ANSWER If the measure.

Warm Up Week 6 1) write an equation that passes through the given point and y-intercept. ( 2, 1 ) ; b = 5.

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

Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.

EXAMPLE 4 Write a biconditional Write the definition of perpendicular lines as a biconditional. SOLUTION Definition: If two lines intersect to form a right.

2-2 Analyze Conditional Statements Hubarth Geometry.

MID CHAPTER 2 QUIZ REVIEW SECTIONS 2.1, 1.4-5, 2.5.

Conditional Statements A conditional statement has two parts, the hypothesis and the conclusion. Written in if-then form: If it is Saturday, then it is.

2.2 Definitions and Biconditional Statements GOAL 1 Recognize and use definitionsGOAL 2 Recognize and use biconditional statements. What you should learn.

Bell Work Find the hypothesis and conclusion 1) If the class behaves, then Mr. Liu will give all the students 5 point extra credit Find the converse 2)

Conditional & Biconditional Statements Chapter 2 Section 2 1.

Biconditional Statements p q. Biconditional Statements p q {P iff q} P, if and only if q Is equivalent to both: If p, then q If q, then p P, if and only.

Conditional & Biconditional Statements Chapter 2 Section 4.

WARM UP 01/09/17 Go over the words and write the Definition of each:

2.2 Definitions and Biconditional Statements

Prerequisite Skills VOCABULARY CHECK Copy and complete the statement.

Classify each of the following angles as acute, right, or obtuse.

2.2 – Analyze Conditional Statements

Classify each of the following angles as acute, right, or obtuse.

Opener 5. If a number greater than 2 is even, then it’s not prime

Chapter 2 Quiz Review.

Definitions and Biconditional Statements

Biconditionals and definitions

EXAMPLE 4 Write a biconditional

EXAMPLE 1 Rewrite a statement in if-then form

Assumptions, Justifications, and Conclusions

2.1 Conditional Statements

Section 2.2 Definitions and Biconditionals

Section 2.2 Definitions and Biconditionals

2.2 Definitions and Biconditional Statements

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Chapter 2.2 Notes: Analyze Conditional Statements

Section 2.2 Definitions and Biconditional Statement

2.1 Continued: Definitions and Biconditionals

Presentation transcript:

2.2 Definitions and Biconditional Statements

Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular to a plane is a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it.

Exercise Decide whether each statement about the diagram is true. Explain your answer using the definitions you have learned. a.Points D, X, and B are collinear. b.AC is perpendicular to DB. c.<AXB is adjacent to <CXD. A B C DX....

Biconditional Statement – It is Saturday, only if I am working at the restaurant. Conditional Statement – If it is Saturday, then I am working at the restaurant.

Consider the following statement x = 3 if and only if x 2 = 9. a.Is this a biconditional statement? Yes a.Is the statement true? No, because x also can be -3.

Rewrite the biconditional as conditional statement and its converse. – Two angles are supplementary if and only if the sum of their measures is 180°. – Conditional: If two angles are supplementary, then the sum of their measures is 180°. – Converse: If the sum of two angles measure 180°, then they are supplementary.

State a counterexample that demonstrates that the converse of the statement is false. – If three points are collinear, then they are coplanar. – If an angle measures 48°, then it is acute.