Geometry Journal 2

1. Geometry Journal 2 Sebastian Busto 9-3

2. Conditional Statement A conditional statement is a statement that establish a necessary condition for a thing that has happen. Examples • If the balloon is inflated then it would fly away. • Converse – If the balloon would fly away then it is inflated. • Inverse – If the balloon isn’t inflated the it wont fly away. • Contrapositive – If the balloon isn’t inflated then it wont fly away.

3. Counter example A counter example is an example that proves that a statement is false. Example • If the balloon fly away then it is inflated • - The balloon flew away, if the wind blow. • If the grass is wet then it rain • - The grass could be wet, if you wet the grass, • If a number is odd the number is prime • - 9

4. Point, Line, and Plane Postulates • Point: A point is an undefined term that describes a location and has no size. • Plane postulates: Through any three non-colinear points there is exactly one plane. • Line: Through any two points there is exactly one line.

5. Definition A Definition is a description of a mathematical concept that can be written as a bi-conditional statement. Perpendicular Lines : Two lines are perpendicular if and only if they intersect at 90˚ A line is perpendicular to a plane if and only if their intersection is exactly at 90˚

6. Bi-Conditional statement A Bi-conditional statement is a statement where both conditions are needed. They are important because they can be used to establish if a definition is true or false. They are used to write definitions. Examples • A angle is acute if and only if it measures less than 90˚ • An angles is obtuse if and only if measures more than 90˚ • A angle is straight if and only if it measures exactly 180˚

7. Deductive reasoning Deductive reasoning : Is the process of using logic to draw conclusions. Symbolic notation: uses letters to represent statements and symbols to represent the connection between them. • P= Today is a school day. Q – I am going to the school. P  Q