Honors Geometry
Chapter 2
Name:______________________
Date:________________
The Structure of Geometry
Geometry is based on a ______________--a system of thought in which conclusions are justified
by means of previously assumed or proved statements.
Every deductive structure contains the following four elements:
1. ______________ _______
2. ______________
3. ______________
4. ______________
Conditional Statements (Implication): is a statement in the form _______________ where __
and__ are declarative statements.
The ____ part is called the __________________.
The ____ part is called the __________________.
__________ can be symbolized 𝑝 → 𝑞 (also read ______________).
Declarative Sentence:
Conditional form (IF, THEN):
The ___________ of any statement p is the statement “_________”. The Symbol for not p is __.
Example:
Conditional Statement: if _____ then _____
Converse Statements: if ______ then ______
Inverse Statement: if ______ then _______
Contrapositive Statement: if _____ then _____
Honors Geometry
Chapter 2
Name:______________________
Date:________________
A ______________ (or ____________) is a statement that is accepted as true without proof.
Definitions are ALWAYS REVERSIBLE!
Example:
Theorems and Postulates: not always reversible.
Example:
*When we start writing proofs, you must memorize postulates, definitions, and theorems in order
to be successful.
Now it’s your turn to try! Identify the Converse, Inverse, and contrapositive of each true
conditional statement. Then decide if the new statement is true or false.
Example 1: If an angle’s measure is 25, then the measure of the angle’s complement is 65.
Example 2: If you live in Chicago, then you live in Illinois.
Example 3: If an angle is a right angle, then it has an angle measure of 90º.