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000 DHS Geometry 1-2

Anderson Ch 1-2: Definitions IFF form

QuestionAnswer
midpoint A point is the midpoint of a segment IF AND ONLY IF it cuts the segment into 2 congruent segments.
perpendicular lines Two lines are perpendicular IF AND ONLY IF they form a right angle.
angle bisector A ray is an angle bisector IF AND ONLY IF it cuts the angle into 2 congruent angles.
congruent angles Two angles are congruent IF AND ONLY IF they have equal measures.
congruent segments Two segments are congruent IF AND ONLY IF they have equal measures.
segment bisector A point, line or ray is a segment bisector IF AND ONLY IF it intersects the segment at its midpoint.
acute angle An angle is an acute angle IF AND ONLY IF its measure is between 0 and 90 (0<m<90).
right angle An angle is a right angle IF AND ONLY IF its measure is 90.
obtuse angle An angle is an obtuse angle IF AND ONLY IF its measure is between 90 and 180 (90<m<180).
complementary angles Two angles are complementary angles IF AND ONLY IF the sum of their measures is 90.
supplementary angles Two angles are supplementary angles IF AND ONLY IF the sum of their measures is 180.
adjacent angles Two angles are adjacent angles IF AND ONLY IF they share a common vertex and side, but have no common interior points.
linear pair Two angles are a linear pair IF AND ONLY IF their non-common sides are opposite rays.
vertical angles Two angles are vertical angles IF AND ONLY IF their sides form two pairs of opposite rays and they are not adjacent.
hypothesis The "if" part of an If...then... statement.
conclusion The "then" part of an If...then... statement.
conditional statement If p, then q.
converse of If p, then q. If q, then p.
inverse of If p, then q. If not p, then not q.
contrapositive of If p, then q. If not q, then not p.
biconditional statement A statement that contains IF AND ONLY IF and represents a conditional statement and its converse.
postulate A statement that is accepted without proof.
theorem A statement that can be proven.
counterexample A specific case for which the conjecture is false.
conjecture An unproven statement that is based on observations.
inductive reasoning Reasoning using observed patterns to form a conjecture.
deductive reasoning Reasoning using facts, definitions, and properties to form a logical argument.
Created by: dekalbmath
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