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When studying Geometry we use: Undefined terms When studying Geometry we use: Undefined terms Assumptions know as postulates or axioms When studying Geometry we use: Undefined terms Assumptions know as postulates or axioms Definitions When studying Geometry we use: Undefined terms Assumptions know as postulates or axioms Definitions Theorems and other conclusions Two undefined terms: point line Postulates or axioms are statements assumed to be true without proof. Postulates or axioms are statements assumed to be true without proof. An example of a postulate: Any segment or angle is congruent to itself. (Reflexive Property) We have looked at two theorems so far: We have looked at two theorems so far: Theorem 1: If two angles are right angles, then they are congruent. We have looked at two theorems so far: Theorem 1: If two angles are right angles, then they are congruent. Theorem 2: If two angles are straight angles, then they are congruent. Among the terms already defined in this set of lessons are: line segment, ray, angle, congruent, acute angle, right angle, obtuse angle, straight angle, polygon, triangle, adjacent angles, union, intersection, collinear, theorem, midpoint, trisection points, angle bisector, angle trisectors, and postulate. Another definition Definition: A definition states the meaning of a term or idea. Definitions can be written as conditional statements. Definitions can be written as conditional statements. Conditional statements are written in the form: If p, then q where p and q are declarative statements. If p, then q The "if" part (p) of a statement is called the hypothesis, and the "then" part (q) is called the conclusion. Another way to write "If p, then q" is Right angle: A right angle is an angle with a measure of 90º. Right angle: A right angle is an angle with a measure of 90º. If an angle is a right angle, then it has a measure of 90º. Right angle: A right angle is an angle with a measure of 90º. If an angle is a right angle, then it has a measure of 90º. Converse: If an angle has a measure of 90º, then it is a right angle. is the converse of is the converse of The converses of all definitions are true statements. The converses of theorems and postulates are not always true. Theorem 1: If two angles are right angles, then they are congruent. Converse is false: If two angles are congruent, then they are right angles. When studying Geometry we use: undefined terms, definitions, postulates, and theorems. When studying Geometry we use: undefined terms, definitions, postulates, and theorems. Definitions can be written as conditional statements . When studying Geometry we use: undefined terms, definitions, postulates, and theorems. Definitions can be written as conditional statements . The converses of all definitions are true. When studying Geometry we use: undefined terms, definitions, postulates, and theorems. Definitions can be written as conditional statements . The converses of all definitions are true. Not all converses of postulates and theorems are true.