Lesson 2 .1: Conditional Statements

Learning GoalsRecognize and analyze a conditional statement.

Write postulates about points, lines, and planes as conditional statements

ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators

ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators

Definition

Conditional StatementA type of statement that can be written in if-then form

The part after the “if” called the hypothesis the part after the “then” is called the conclusion

To do well in Geometry, you must study.

If you want to do well in Geometry,then you must study.

Rewrite the conditional statement in if-then form.

example

If you want to do well in Geometry, then you must study.

hypothesis:

conclusion:

You want to do well in Geometry.

You must study.

Identify the hypothesis and conclusion.

All mammals breathe oxygen.conditional statement:

If an animal is a mammal, then it breathes oxygen.

hypothesis:

conclusion:

You Try

An animal is a mammal

It breathes oxygen

A blue sky means no rain today.conditional statement:

If the sky is blue, then it will not rain today

hypothesis:

conclusion:

You Try

The sky is blue.

It will not rain today.

properties

Converse A conditional statement with the hypothesis and conclusion reversed.

If you want to do well in Geometry, then you must study.

If you study,then you will do well in Geometry.

You Try

Write the converse, If an animal is a fish, then it can swim.

If an animal can swim, then it is a fish.

true or false?FALSE

Write the converse

30A m A If is acute, then .

You Try

30 , .m A A Ift hen is acute

true or false?FALSE

properties

A conditional statement, or conjecture, is true only when every possible case of thestatement is true.To show a statement is false only one example showing the statement doesn’t work is needed.The example is called a counterexample.

In a counterexample the hypothesis is true, but the conclusion is false.

every time something involving a statement happens

Write the converse

30A m A If is acute, then .

You Try

30 , .m A A Ift hen is acute

true or false?FALSE

counterexample:

Counterexample

Show the following conjecture is false by finding a counterexample.

The difference of two positive numbers is always positive.

If-then form:

Counterexample:

4 7 3 is negative making the the conclusion false.

4 7Let the two numbers be and .

If two positive numbers are subtracted,then the answer will be positive.

Points, Lines, and Planes Postulates

Through any two points, there exists exactly one line.

A

B

If two points exist, then exactly one line can be drawn through the points.

Points, Lines, and Planes Postulates

A line

A

B

If a line exists, then at least two points are on the line.

contains at least two points

This Postulate is the ___ of the last postulate.

a) conditionalb) converse

Points, Lines, and Planes Postulates

If two lines intersect,then their intersection is exactly one point.

P

Points, Lines, and Planes Postulates

Through any three noncollinear points there exists exactly one plane.

P

R

Q

Points, Lines, and Planes Postulates

A plane contains at least three noncollinear points.

a) conditionalb) converse

P

R

Q

This Postulate is the ___ of the last postulate.

Points, Lines, and Planes Postulates

If two points lie in a plane, then the line containing them is also on the plane.

P

Q

Points, Lines, and Planes Postulates

If two planes intersect, then their intersection is a line.

N

M

N

M

Today’s Assignment

p. 8: 34 – 39 p. 75 : 2, 9, 11, 14, 15, 18, 35 – 38