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Geometry Journal 2

This article delves into the essential concepts of conditional statements, definitions, and deductive reasoning in geometry. A conditional statement establishes a necessary condition, illustrated by examples related to balloon inflation and grass wetness. It explores the converse, inverse, and contrapositive forms, alongside counterexamples to highlight potential fallacies. Additionally, it explains definitions as bi-conditional statements, exemplifying various angle classifications. Lastly, it introduces deductive reasoning and symbolic notation, essential tools for logical conclusions in geometric reasoning.

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Geometry Journal 2

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  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

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