Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Geometry Name: _________________________ Date: _______________ Per.: ______ MIDTERM EXAM: Chapter 2 Review Vocabulary Conditional Statements Negation If-then form Hypothesis Conclusion Converse Inverse Contrapositive Equivalent statement Perpendicular lines Line perpendicular to a plane Biconditional statements Logical argument Two-column proof Law of Detachment Law of Syllogism Theorem Paragraph proof Key Concepts & Skills Write statements in if-then format; identify the hypothesis and conclusion Write the converse, inverse, and contrapositive of a conditional statement. Give a counterexample to disprove a statement. Rewrite a bi-conditional statement as a conditional and its converse Identify whether reasoning used is inductive or deductive Find next items in a pattern Use the Laws of Detachment and Syllogism to draw a conclusion from given statement(s) Identify the algebraic property illustrated by a statement. Solve equations and state a reason for each step. Write two-column proofs proving statements about segments and angles. Key Points Conditional Inverse Converse Contrapositive if – then negate conditional switch conditional’s “if” and “then” negate converse pq ~p ~q qp ~q ~p Inductive reasoning: patterns, observation, experience Deductive reasoning: fact-based Law of Detachment Given p q Hypothesis happens Conclusion occurs Law of Syllogism If p q and q r, then p r (similar in logic to transitive property) MD/CR/1-12/Ch. 2 MT Review 1 Geometry Practice Problems I. Conditional Statements Write the statement in if-then form. Determine the hypothesis and conclusion, and write the inverse, converse, and contrapositive. The game will start at 4:00 if the other team arrives within five minutes. II. Biconditional Statements Write the biconditional statement as a conditional and its converse. A number is divisible by 10 if and only if it ends in 0. III. Solve for the variable using the given information. 1) B) IV. Proving Statements about Segments and Angles 1) 2) MD/CR/1-12/Ch. 2 MT Review 2 Geometry 3) IV. Algebraic Properties - Identify the property. mÐS = 45o , then mÐS + 45o = 90o . 1) If 2) If UV = VW, then VW = UV. 3) If AE = EG and EG = JK, then AE = JK. 4) If mÐK = 9o , then 3(mÐK ) = 27o V. Solve for x 1) 3) Find the measure of the missing angles. MD/CR/1-12/Ch. 2 MT Review 2) 4) Find the measure of angles 1 and 2. 3 Geometry VI. Use the Law of Syllogism or the Law of Detachment to write a valid conclusion. If you cannot make a valid conclusion, write INVALID. a) If the newspaper club meets today, then it is Thursday If today is Thursday, then the garbage going out. b) If it is summer, then school is closed. School is closed. c) If an angle measures less than 90, then it is an acute angle. mA = 42 d) If the sum of two angles is 180, then they are supplementary If two angles form a linear pair they are supplementary. VII. Proofs For #1-3 Use the following Diagram. 1) Given: m Ð1 = m Ð2 m Ð3 = m Ð4 Prove: m ÐSRT = m ÐSTR 2) Given: RP = TQ PS = QS Prove: RS = TS 3) Given: m ÐSRT = m ÐSTR m Ð3 = m Ð4 4) Given: Ð3 is supplementary to Ð1 Ð4 is supplementary to Ð2 Prove: Ð3 @ Ð4 Given: AC ^ BC Prove: Ð3 @ Ð2 5) Prove: m Ð1 = m Ð2 Ð3 is complementary to Ð1 MD/CR/1-12/Ch. 2 MT Review 4