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2.1 Conditional Statements

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Page 1: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

2.1 Conditional Statements

Page 2: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Conditional Statement

Conditional statement has two parts, hypothesis and a conclusion.

If _____________, then____________.hypothesis conclusion

Page 3: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Rewrite in If-Then form

A number divisible by 9 is also divisible by 3. If a number is divisible by 9, then it is divisible

by 3.

Two points are collinear if they lie on the same line. If two points lie on the same line, then they are

collinear.

Page 4: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Writing a Counterexample

Write a counterexample to show that the following conditional statement is false. If x2 = 16, then x = 4.

Page 5: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Converse

Two points are collinear if they lie on the same line.

If two points are collinear, then they lie on the same line.

If two points lie on the same line, then they are collinear.

Conditional Statement

Converse

Page 6: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

A statement can be altered by negation, that is, by writing the negative of the statement. Statement: m<A = 30° Negation: m < A ≠ 30°

Statement: <A is acute. Negation: <A is not acute.

Page 7: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Inverse

If two points lie on the same line, then they are collinear.

If two points do not lie on the same line, then they are not collinear.

Conditional

Inverse

Page 8: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Contrapositive

If two points lie on the same line, then they are collinear.

If two points are not collinear, then they do not lie on the same line.

Conditional

Contrapositive

Page 9: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

When two statements are both true or both false, they are called equivalent statements. A conditional statement is equivalent to its

contrapositive. The inverse and converse of any conditional

statement are equivalent.

Page 10: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Write the a) inverse b) converse c) contrapositive

If there is snow on the ground, then flowers are not in bloom.

a) If there is no snow on the ground, then flowers are in bloom.

b) If flowers are not in bloom, then there is snow on the ground.

c) If flowers are in bloom, then there is no snow on the ground.

Page 11: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Point, Line, and Plane Postulates

Postulate 5

Through any two points there exists exactly

one line.

Postulate 6

A line contains at least two points.

Postulate 7

If two lines intersect, then their intersection is

exactly one point.

Page 12: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Postulate 8

Through any three noncollinear points there

exists exactly one plane.

Postulate 9

A plane contains at least three noncollinear

points.

Postulate 10

If two points lie in a plane, then the line

containing them lies in the plane.

Page 13: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Postulate 11 If two planes intersect, then their intersection

is a line.

Page 14: 2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

Review

Write the converse of the conditional statement.

If x = 3, then y = 7.

If Carrie joins the softball team, then Mary will

join.

If two angles are vertical, then their measures

are equal.


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