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Postulates, Theorems & Definitions

Congruent segments Line segments that have the exact same length, shape or size.
Postulate #1: Ruler postulate The distance between one point to another (absolute value) [x2 - x1]
Postulate #2: Segment addition postulate If B is between A and C, then AB+BC=AC
Postulate #3: Protractor Postulate When you line up a protractor at 0 degrees, the angle measure lines up with that on the protractor
Postulate #4: Angle addition postulate If D is the interior of <ABC, then <ABD+<DBC+<ABC
Postulate #5: through any 2 points there exists exactly one line
Postulate #6 A line contains at least 2 points
Postulate #7 If 2 lines intersect, then there intersection is exactly one point
Postulate #8 through any 3 noncollinear points there exists exactly one plane
Postulate #9 A plane contains at least three noncollinear points
Postulate #10 if 2 points lie on a plane, then the line they lie on lies on the plane
Postulate #11 If 2 planes intersect, then there intersection is a line
Postulate #12: Linear Pair Postulate If 2 angles are a linear pair, then they are supplementary
Midpoint Point that divides a segment into 2 congruent segments
Segment Bisector a point, ray, line, line segment, or plane that intersects the segment at its midpoint.
Right angle measure of angle = 90 degrees
Straight angle measure of angle = 180 degrees
Acute angle Measure of angle is less than 90 degrees, and more than 0
Obtuse angle Measure of angle is greater than 90 degrees, but less than 180 degrees
Congruent angles Angles with the exact same measurement
Angle Bisector A ray that divides an angle into 2 congruent angles
Complementary Angles The sum of 2 angles is 90 degrees
Supplementary Angles 2 angles with the sum of 180 degrees
Adjacent Angles Share a common side and vertex, no interior point
Linear pair If there non common sides are opposite rays
Vertical Angles The sides form 2 pairs of opposite rays
Conjecture An unproven statement based on observation
Inductive reasoning When you find a pattern in specific cases, write a conjecture
Counterexample A specific example/case proving the conjecture wrong
Conditional Statement A logical statement that has 2 parts, a hypothesis and a conclusion
If-then form If hypothesis, then conclusion. "If A, then B"
Converse If conclusion, then hypothesis.
Inverse If not The hypothesis, then not the conclusion
Contrapositive If not the conclusion, then not the hypothesis
Biconditional statement If and only if...
Negation the opposite of the original statement.
Equivalent statement When 2 statements are both true and both false
Perpendicular lines 2 lines intersect and form a right angle
Law of detachment If the converse is true then the conclusion is also true
Law of syllogism If a, then b. If b, then c. If A, then c.
Substitution Property If a=b, then a can be substituted for b in any equation or expression
Distributive property a(b+c) = ab+ac
Do the reflexive, symmetric, and transitive properties of equality pertain to measurement of angles and segments or congruence? The properties of equality pertain to measurements
Theorem 2.1: Congruence of segments Is reflexive, symmetric, and transitive. Pertains to congruence
Theorem 2.2: Congruence of angles Is reflexive, symmetric, and transitive. Pertains to congruence (Symmetric property of segment congruence)
Theorem 2.3: Right angles congruence theorem All right angles are congruent
Theorem 2.4: Congruent supplements theorem If 2 angles are supplementary to the same angle, then they are congruent
Theorem 2.5: Congruent complements theorem If 2 angles are complementary to the same angle, then they are congruent
Theorem 2.6: Vertical Angles congruence theorem Vertical angles are congruent
Created by: jill_genova