![]() ![]() ⭕️Common Segments Theorem If given four collinear points that are arranged so two of the points are the same distance away from each other as the other two, then the distances between the first and third points and the second and fourth points are equal. □Law of Syllogism If p->q, and q->r, then p->r. □Law of Detachment If a conditional is true and its hypothesis is true, then its conclusion is true. □Deductive Reasoning To conclude something is true based on facts, definitions, and theorems. □Contrapositive The statement formed by the exchanging AND negation of the hypothesis and conclusion. □Inverse The statement formed by the negation of the hypothesis and conclusion. □Converse The statement formed by exchanging the hypothesis and conclusion. □Counterexample One example in which a conjecture is proved not to be true. □Conjecture A statement that is believed to be true based on inductive reasoning. □Inductive Reasoning Reasoning from one or more specific experiences or facts to reach a general conclusion. □Linear Pair A pair of adjacent angles whose noncommon sides are opposite rays. □Adjacent Angles Angles that have a common side and a common vertex (corner point), but no common interior points. □Midpoint A point that divides a segment into two congruent segments. □Congruent Segments Line Segments with the same length. □Congruent Figures Figures that have the same size and shape. □Congruent Circles Circles with congruent radii. □Congruent Angles Angles that have the same measure. □Coplanar Points Points that lie in the same plane. □Collinear Points Points that lie on the same line. □Complementary Angles Two angles whose sum is 90 degrees. □Supplementary Angles Two angles whose sum is 180 degrees. □Theorem A mathematical statement which we can prove to be true. ⭕️Congruent Complements Theorem If two angles are complementary to the same angle (or to two congruent angles), then the two angles are congruent. ⭕️Right Angle Congruence Theorem If there are right angles, then they are congruent. ⭕️Congruent Supplements Theorem If two angles are supplementary to the same angle (or to two other congruent angles), then the two angles are congruent. ⭕️Linear Pair Theorem If two angles form a liner pair, then they are supplementary. ![]() ⭕️Distributive Property of Equality If a(b+c), then it = ab+ac. ⭕️Transitive Property of Congruence If Figure A is congruent to Figure B and Figure B is congruent to Figure C, then Figure A is congruent to Figure C (L.O.S). ![]() (Look in a mirror - reflection) ⭕️Symmetric Property of Congruence If Figure A is congruent to Figure B, then Figure B is congruent to Figure A. ⭕️Reflexive Property of Congruence Figure A is congruent to Figure A. ⭕️Substitution Property of Equality If a = b, then b can be substituted for a in any expression. ⭕️Transitive Property of Equality If a = b and b = c, then a = c (L.O.S.). ⭕️Reflexive Property of Equality a = a (Look in a mirror - reflection) ⭕️Symmetric Property of Equality If a = b, then b = a. ⭕️Division Property of Equality If a = b and c is not equal to 0, then a/c = b/c. ⭕️Multiplication Property of Equality If a = b, then ac = bc. ⭕️Subtraction Property of Equality If a = b, then a - c = b - c. □Angle Addition Postulate If S is in the interior of L PQR, then mL PQS+mL PQR = mL PQR ⭕️Addition Property of Equality If a = b, then a + c = b + c. □Protractor Postulate If there is a line and a point on the line, then all rays that can be drawn from the point can be put into a one to one correspondence with all real numbers 1 to 180. □Exterior of an angle The set of all points outside the angle. ![]()
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