Undefined terms Intuitive concepts not explicitly defined since they define themselves. The 3 undefined terms are: point, line, plane Point Location, without a size. Represented by a dot. Line Infinite number of points on a straight path extending infinitely in two directions. Plane Infinite number of points on a flat surface extending infinitely in three directions. Segment A finite piece of a line Ray A piece of a line that extends infinitely in only one direction. Opposite Rays Two rays on the same line with the same endpoint and extend in opposite directions. Angle Geometric figure formed by 2 rays with one common endpoint. Endpoint the point(s) on the end of a segment or ray Collinear points Points all in one line (can draw a line through all of them at once) Postulate True statement that is accepted without proof; used as a basis to prove other things (synonym: axiom) Segment Addition Postulate If points A, B, and C are collinear and B is between A & C, then AB + BC = AC. Acute angle Measures between 0 and 90 degrees. Right angle Measures 90 degrees. Obtuse angle Measures between 90 and 180 degrees. Straight angle Measures 180 degrees. Angle Addition Postulate If point B lies in the interior of ∠ AOC, then m ∠ AOB + m ∠ BOC = m ∠ AOC. Congruent Same shape, same size - Having the same measurement or length. Perpendicular bisector of a segment A line, segment, or ray that is perpendicular to the segment and divides the segment into two congruent segments. Angle bisector A ray that divides an angle into two congruent angles. Midpoint of a segment A point that divides the segment into 2 congruent segments 𝑥 Midpoint Formula Distance Formula Inductive reasoning (Honors Only) 2 𝑑 𝑥 𝑥 𝑦 , 𝑥 𝑦 2 𝑦 𝑦 Reaching conclusions based on a pattern of specific examples of past events Deductive reasoning Uses logical steps based on given facts to reach a conclusion. A counterexample An example that proves a statement false. Conditional Statements An “If-Then” statement with a hypothesis & conclusion (if p, then q) The converse of a Exchange the hypothesis and the conclusion. (if q, then conditional statement p) The negation of a Opposite meaning of the original statement. (not p) conditional statement The inverse of a Negate both the hypothesis and the conclusion of a conditional statement statement. If not p, then not q. The contrapositive of a conditional statement Biconditional statement Negate and reverse both the hypothesis and the conclusion of a statement. If not q, then not p. Addition Property If a = b and c = d, then a+c=b+d Subtraction Property If a = b and c = d, then a - c = b - d. Multiplication Property Division Property If a = b, then ca = cb. The statement & its converse are both true. They can be combined using the words if and only if. If a = b and c ≠ 0, then a ÷ c = b ÷ c Reflexive property a=a Symmetric Property If a = b, then b = a Transitive Property If a = b and b = c, then a = c Substitution Property If a = b, then either a or b may be substituted for the other in any equation (or inequality) Distributive Property a (b + c) = ab + ac Complementary angles Supplementary angles Linear pair Angles whose measures add up to 90°. Adjacent angles whose edges form a line. Definition of congruent angles Angles are congruent iff their measurements are equal. Theorem A statement that must be proven Angles whose measures add up to 180°. Definition of Midpoint If B is the midpoint of 𝐴𝐶 , then 𝐴𝐵 ≅ 𝐵𝐶 & AB = BC. Definition of Angle Bisector If 𝐵𝐷⃗ bisects ∠ ABC, then ∠ ABD ≅ ∠ DBC and m ∠ ABD = m ∠ DBC. Vertical Angle Theorem If 2 angles are vertical angles, then they are congruent to each other (measurements are equal). Linear Pair Theorem If 2 angles form a linear pair, then they are supplementary to each other.