Chapter 2: Geometric Reasoning Review
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1 Geometry B Name: Date: Block: Chapter 2: Geometric Reasoning Review Show all work to receive full credit. This will be collected. 1) What is the next item in the pattern? 1, 2, 4, 8,... 2) Find the next item in the pattern. 2, 5, 8, 11, 14,... 3) Does each conclusion use inductive or deductive reasoning? a) The sum of the angle measures of a triangle is 180. Two angles of a triangle measure 40 and 60, so Kandy concludes that the third angle measures 80. b) All of the students in Henry s Geometry class are juniors. Alexander takes Geometry, but has another teacher. Henry concludes that Alexander is also a junior. 4) Given: If Lewis earns a scholarship, he can go to college. Lewis earns a scholarship. Conjecture: Lewis can go to college. Determine whether the conjecture is valid by the Law of Detachment. 5) Which symbolic statement represents the Law of Syllogism? A If p q and q r are true statements, then p r is a true statement. B If p q and p r are true statements, then q r is a true statement. C If p q and r q are true statements, then q p is a true statement. D If p r and q r are true statements, then p q is a true statement.
2 6) Given: If a whole number ends in 0, then it is divisible by 2. If a whole number is divisible by 2, then it is even. Conjecture: If a whole number ends in 0, then it is an even number. Determine whether the conjecture is valid by the Law of Syllogism. 7) Given: All snarfs are yelbs. All yelbs are blue. Migs can be either green or pink. Some slokes are snarfs. What conclusion can be drawn? A Some migs are snarfs. C Some slokes are yelbs. B Some snarfs are green. D All slokes are migs. 8) Identify the hypothesis and conclusion of the conditional. A triangle with one angle measure of 120 degrees is an obtuse triangle. (write in if, then format to make it easier) 9) Given the conditional statement If it is January, then it is winter in the United States, which is true? F the converse of the conditional G the inverse of the conditional H the contrapositive of the conditional J Not here 10) Identify the hypothesis and conclusion of the conditional. All prime numbers are divisible by 1 and itself.
3 11) What is the inverse of the conditional statement If a number is divisible by 6, then it is divisible by 3? 12) Determine if the statement If n 2 = 100, then n = 10. is true. If false, provide a counterexample. 13) Determine if the bi-conditional is true or false. If false provide a counterexample. Two angles are supplementary if and only if they are both right angles. 14) Write the converse, inverse, and contra positive of the conditional statement If Chad was born in 1998, then he was born in the 90 s decade. Find the truth value of each. Converse: Inverse: Contrapositive 15) For the conditional If an angle is a straight angle, then its measure is 180 degrees. write the converse and the bi-conditional. Converse: Biconditional:
4 16) Determine if the bi-conditional Two angles are supplementary if and only if one is acute and one is obtuse. is true. If false, give a counterexample. 17) Write the definition An equilateral triangle is a triangle with three angles each measuring 60 degrees. as a bi-conditional. 18) Solve the equation. Show all your steps and write a justification for each step. (Remember to simplify after every operation.) 1 a ) Solve each equation. Write a justification for each step. m - 8 = 13 4y - 1 = 27
5 20) Given: m 1 = 30 and m 2 = 2m 1. Prove: 1 and 2 are complementary. Statements Reasons Substitution POE 4. Simplify. 5. Addition POE 6. Simplify ) Given: B is midpoint of AC C is midpoint of BD Prove: AB CD A B C D Statement Reason definition of a midpoint Transitive POC
6 22) Given: 1 and 2 are right angles Prove: Statement Reason definition of a right angle Transitive POC The above proof can be done in 2 steps (5 steps is the long way) both are correct. Do both Statement Reason ) Use the Law of Syllogism to draw a conclusion from the given information. Given: If one angle of a triangle is 90, then the triangle is a right triangle. If a triangle is a right triangle, then its acute angle measures are complementary. If one angle of a triangle is 90, then its acute angle measures are complementary.
7 24) Use the given flowchart proof to write a two-column proof. Given: B is the midpoint of AC and AD = EC Prove: DB = BE Statements Reasons 25) Use the given paragraph proof to write a two-column proof. Given: 2 4 Prove: 1 3 Paragraph proof: By the Vertical Angles Theorem, 1 2, and 3 4. It is given that 2 4. By the Transitive Property of Congruence, 1 4, and thus 1 3. Statements Reasons
8 Define the following postulates, theorems, and definitions. Segment Addition Postulate Angle Addition Postulate Linear Pair Theorem Congruent Supplements Theorem Right Angle Congruence Theorem Congruent Complements Theorem Common Segments Theorem Vertical Angle Theorem Definition of a midpoint Definition of congruent angles Definition of congruent segments Definition of supplementary angles
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