Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Published byGarry Cooper Modified over 9 years ago

Similar presentations

Presentation on theme: "2.2 Definitions and Biconditional Statements. Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular."— Presentation transcript:

1 2.2 Definitions and Biconditional Statements

2 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.

3 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....

4 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.

5 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.

6 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.

7 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.

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

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.

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.
If-Then Statements 2-1.

If-Then Statements 2-1.
Biconditionals & Counterexamples Geometry Chapter 02 A BowerPoint Presentation.

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.

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

Notes on Logic Continued
Conditional Statements

Conditional Statements
Unit 3 Lesson 2.2: Biconditionals

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.

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

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.

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.

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.

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

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

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.

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.

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.

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.

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

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.

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

Similar presentations

Ads by Google