Geometry Study Sheet Chapter 2 by Tristen Wallace https://padlet.com/20wallacetl/d4u9g0r97kby Includes all of the key terms and three example problems from Chapter 2. en-us 2016-12-13 03:05:16 UTC 2024-06-04 13:59:02 UTC hello@padlet.com inductive reasoning: reasoning based on patterns one observes 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520069 2016-12-14 04:18:09 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520069 conjecture: a conclusion one reaches using inductive reasoning 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520172 2016-12-14 04:20:38 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520172 counterexample: an example that shows that a conjecture is incorrect 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520200 2016-12-14 04:21:19 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520200 conditional: an if-then statement 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520289 2016-12-14 04:22:40 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520289 hypothesis: the part p following if 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520309 2016-12-14 04:22:53 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520309 conclusion: the part q following then 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520323 2016-12-14 04:22:59 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520323 truth value: true or false of a conditional 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520380 2016-12-14 04:23:49 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520380 negation: the opposite of the statement represented with -p or "not p" 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520405 2016-12-14 04:24:31 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520405 converse: exchange the hypothesis and the conclusion 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520445 2016-12-14 04:25:23 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520445 inverse: negate both the hypothesis and the conclusion of the conditional 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520472 2016-12-14 04:25:47 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520472 contrapositive: negate both the hypothesis and the conclusion of the converse 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520474 2016-12-14 04:25:53 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520474 equivalent statements: statements of the same truth value 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520496 2016-12-14 04:26:24 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520496 biconditional: a single true statement that combines a true conditional and its true converse (used 2 parts of each conditional with the phrase if and only if) 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520516 2016-12-14 04:27:00 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520516 deductive reasoning: the process of reasoning logically from given statements or facts to a conclusion 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520578 2016-12-14 04:28:02 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520578 Law of Detachment 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520616 If the hypothesis of a true conditional is true, then the conclusion is true]]> 2016-12-14 04:28:51 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520616 Law of Syllogism 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520636 Allows one to state a conclusion from the 2 true conditional statements when the conclusion of one statement is the hypothesis of the other statement]]> 2016-12-14 04:29:16 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520636 addition property: if a = b, then a+c = b+c 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520688 2016-12-14 04:30:55 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520688 subtraction property: if a = b, then a-c = b-c 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520720 2016-12-14 04:31:42 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520720 multiplication property: if a = b, then a*c = b*c 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520740 2016-12-14 04:32:09 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520740 division property: if a = b and c does not = 0, then a/c = b/c 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520768 2016-12-14 04:32:50 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520768 reflexive property: a= a 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520797 2016-12-14 04:33:27 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520797 symmetric property: if a = b, then b = a 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520806 2016-12-14 04:33:47 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520806 transitive property: if a = b and b = c, then a = c 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520826 2016-12-14 04:34:10 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520826 substitution property: if a = b, then b can replace a in any expression 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520843 2016-12-14 04:34:50 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520843 The Distributive Property 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520873 Use multiplication to distribute a to each term of the sum or difference within the parentheses]]> 2016-12-14 04:35:30 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520873 properties of congruence: reflexive property, symmetric property, and transitive property 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520904 2016-12-14 04:36:24 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520904 proof: a convincing argument that uses deductive reasoning and shows why a conjecture is true 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520931 2016-12-14 04:37:03 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520931 two-column proof: lists each statement on the left and justification for each statement on the right 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520954 2016-12-14 04:37:40 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520954 theorem: a conjecture or statement that one proves true 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520983 2016-12-14 04:38:42 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143520983 Vertical Angles Theorem (2-1) 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521011 Vertical angles are congruent ]]> 2016-12-14 04:39:23 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521011 paragraph proof: sentences in a paragraph that shows the logical steps in solving a problem with statements and reasons 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521035 2016-12-14 04:39:57 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521035 Congruent Supplements Theorem (2-2) 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521071 If 2 angles are supplements of the same angle (or of congruent angles), then the 2 angles are congruent]]> 2016-12-14 04:40:53 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521071 Congruent Complements Theorem (2-3) 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521133 If 2 angles are complements of the same angle (or of congruent angles), then the 2 angles are congruent]]> 2016-12-14 04:42:00 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521133 Theorem 2-4 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521161 All right angles are congruent]]> 2016-12-14 04:42:43 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521161 Theorem 2-5 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521180 If 2 angles are congruent and supplementary, then each is a right angle]]> 2016-12-14 04:43:01 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521180 Writing Conditional Example Problem #1 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521294 2016-12-14 04:45:17 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521294 Law of Syllogism Example Problem #2 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521410 2016-12-14 04:47:46 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521410 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521414 2016-12-14 04:47:50 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521414 Law of Detachment Example Problem #3 20wallacetl https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521504 2016-12-14 04:49:55 UTC https://padlet.com/20wallacetl/d4u9g0r97kby/wish/143521504