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Conditional Statements Section 2.1

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Conditional statement

A logical statement with two parts: a hypothesis and a conclusion.

Ex.

If it is noon in Georgia, then it is 9 am in California.

HypothesisConclusion

Geometry - Section 2.1: Conditional Statements

Example 1

Example 2

Rewrite the conditional statement in if-then form.

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

B. All sharks have a boneless skeleton.

C. A number divisible by 9 is also divisible by 3.

Write a counterexample to show that the following conditional statement is false.

If x2 = 16, then x = 4.

Geometry - Section 2.1: Conditional Statements

converse

Example 3

The converse of a conditional statements is formed by switching the hypothesis and the conclusion.

Statement

If you see lightning, then you hear thunder.

Converse

If you hear thunder, then you see lightning.

Write the converse of the following conditional statement.

If two segments are congruent, then they have the same length.

Geometry - Section 2.1: Conditional Statements

Negations

inverse

contrapositive

To write the negative of a statement.

A statement that negates the hypothesis and the conclusion of a conditional statement.

A statement that negates the hypothesis and the conclusion of a converse of a conditional statement.

Example 4

Write the (a) inverse, (b) converse, and (c) contrapositive of the statement.

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

Geometry - Section 2.1: Conditional Statements

Postulate 5

Postulate 6

Postulate 7

Postulate 8

Postulate 9

Postulate 10

Postulate 11

Point, Line, and Plane Postulates

Through any two points there exists exactly one line.

A line contains at least two points.

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

Through any three noncollinear points there exists exactly one plane.

A plane contains at least three noncollinear points.

If two points lie in a plane, then the line containing them lies in the plane.

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

NOTE: Use your book to find these, p. 73.

Geometry - Section 2.1: Conditional Statements

Summary

- Today we discussed conditional statements, which are usually in if-then form.
- We learned what a converse, an inverse, and a contrapositive statement is.
- In a converse you switch the hypothesis and conclusion, and in an inverse you negate, and for a contrapositive you switch and negate.
- We discussed what negate means (to write the opposite).
- We learned new postulates about lines and planes.

Geometry - Section 2.1: Conditional Statements

Summary

- Today’s lesson was about conditional statements.
- We learned about converses (switch the hypothesis and the conclusion of the statement).
- I learned that negating means to write the opposite. For example, girls are evil becomes girls are good.
- We learned how these statements relate to math, like “If x2 = 16, then x = 4”
- We learned about inverses (negating), contrapositive.(switching and negating).

Geometry - Section 2.1: Conditional Statements

- Today’s lesson was about conditional statements.
- Conditional statements have hypothesis and conclusions.
- There are different ways to know your hypothesis and conclusions.
- We learned how to rewrite conditional statements in if-then form.
- To find the converse of a statement switch the hypothesis and conclusion.

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Geometry - Section 2.1: Conditional Statements