Geometry Unit 2 - Reasoning and Proof PRACTICE TEST FULLY SOLVED WITH ALL VERIFIED SOLUTIONS

Inductive Reasoning Uses patterns and observations to form conjectures. Conjecture An unproven statement based on observations that is believed to be true. Counterexample An example that proves that a conjecture or statement is false. Conditional Statement A statement that can be written in the form if p, then q where p is the hypothesis and q is the conclusion. Hypothesis The "p" part of a conditional statement. Follows the word if. Conclusion The "q" part of a conditional statement. Follows the word then. Negation The opposite of the original statement. Converse definition Swap the hypothesis and the conclusion if q, then p Inverse definition Negate the hypothesis and the conclusion if ~p, then ~q Contrapositive definition Swap and Negate the hypothesis and the conclusion. if ~q, then ~p Deductive Reasoning Uses facts, definitions, and laws of logic to form a logical argument. Law of Detachment If the hypothesis of a true conditional statement is true, then the conclusion is also true. Law of Syllogism If the hypothesis of one conditional statement is the same as the conclusion of another conditional statement, then a new statement, then you can create a new conditional statement from the pieces that do not overlap. Converse Conditional: If I do my homework, then I get my allowance. __________:"If I get my allowance then I do my homework." Inverse Conditional: If I do my homework then I get my allowance. __________:"If I don't do my homework then I don't get my allowance." Contrapositive Conditional: If I do my homework then I get my allowance. __________:"If I don't get my allowance then I don't do my homework." (Please don't say that to your parents.) Converse Conditional: If P then Q __________:"If Q then P" Inverse Conditional: If P then Q __________:"If not P then not Q" Contrapositive Conditional: If P then Q. __________:"If not Q then not P" Converse Conditional: If two angles are congruent, then they have the same measure. __________:"If two angles have the same measure, then they are congruent." Inverse Conditional: If two angles are congruent, then they have the same measure. __________:"If two angles are not congruent, then they don't have the same measure." Contrapositive Conditional: If two angles are congruent, then they have the same measure. __________:"If two angles don't have the same measure then they are not congruent." Converse Conditional: If a whole number is even then it is a multiple of two. __________:"If a whole number is a multiple of two then it is even. Inverse Conditional: If a whole number is even then it is a multiple of two. __________:"If a whole number is not even then it is a multiple of two." Contrapositive Conditional: If a whole number is even then it is a multiple of two. __________:"If a whole number not a multiple of two then it is not even." Add or remove terms