2, 10, 30, 68, 130,...

Transcription

1 Geometry Unit 4: Reasoning Unit 4 Review Mathematician: Period: Target 1: Discover patterns in a sequence of numbers and figures Directions: Determine what type of is displayed in the given tables. 1) 2) 1, 9, 17, 25,... 2, 9, 28, 65, ) x y B) Quadratic C) Cubic B) Quadratic C) Cubic Directions: Find the sum of the 6 th and 7 th term of the sequence. 4) 5) 3, 14, 33, 60, 95 2, 10, 30, 68, 130,... B) Quadratic C) Cubic 6) 5, 8, 11, 14, 17 6 th term: 7 th term: 6 th term: 7 th term: Directions: Find the value of x that completes the sequence. 6 th term: 7 th term: 7) 2, 22, 62, 118, 190, x, 382, 8) 2, x, 4, 7, 10, 13 x = x = Directions: Draw and determine the number of figures in the iteration. 9) Number of shaded(grey) triangles 10) Number of shaded (grey hexagons) Original Iteration 1 Iteration 2 n =4: Original Iteration 1 Iteration 2 Iteration 4:

2 Target 2: Conditional Directions: Given the following statements, determine the conditional, converse, inverse, and contrapositive. Then find the truth-value. 11) A number is evenly divisible by 9, it is also evenly divisible by 3. True/False Conditional Converse Inverse Contrapositive 12) Panthers live in the forest. True/False Conditional Converse Inverse Contrapositive Directions: Use the conditional statement to write the indicated statement. Then determine the truth-value. 13) If two angles are supplementary, then their sum is 180. Write the inverse statement. Then determine the truth-value. 14) If you live in Illinois, then you live in Chicago. Write the contrapositive statement. Then determine the truth-value. 15) If two numbers are odd then, their sum will be even. Write the converse statement. Then determine the truth value. Directions: Determine if the following statements represent a biconditional. If yes, write the biconditional statement. If not, explain why is does not represent a biconditional. 16) If point divides two congruent segments, then it is a midpoint. Y or N: 17) If Sam lives in Chicago, then she lives in Illinois. Y or N: Determine if the following statement is true or false. If false, provide a counter example 18) If you are an athlete with skates, then you play hockey. T or F: 19) If the conditional statement is true, what other statement will always be true? 20) If a biconditional statement exists, which two statements have to be true? 21) If the contrapositive statement is true what other statement will always be true?

3 Target 3: Use deductive reasoning to make conclusions. Directions: Complete the following two-column proofs. 22) Given: 3 (x 5 ) = 1 3 Prove: x = 2 (1) 3 (x 5 ) = 1 3 (1) (2) 3x 5 = 1 (2) (3) 3x = 6 (3) (4) x = 2 (4) 23) Given: AB = DE, BC = EF Prove: AC = DF (1) Question a A B C D E F (1) Given (2) Question b A B C D E F (2) Segment Addition Postulate (3) Question c A B C D E F (3) Segment Addition Postulate (4) Question d A B C D E F (4) Substitution Property of Equality (5) Question e A B C D E F (5) Substitution Property of Equality (6) Question f A B C D E F (6) Substitution Property of Equality A) DE + BC = DF B) DE + BC = AC C) AC = DF D) AB + BC = AC E) DE + EF = DF F) AB = DE, BC = EF 24) Given: 4b 12 = 8(3b + 1) Prove: b = 1 (1) Question a A B C D E (1) Given (2) Question b A B C D E (2) Distributive Property of Equality (3) Question c A B C D E (3) Subtraction Property of Equality (4) Question d A B C D E (4) Subtraction Property of Equality (5) Question e A B C D E (5) Division Property of Equality A) 12 = 20b + 8 B) 4b 12 = 8(3b + 1) C) b = 1 D) 20 = 20b E) 4b 12 = 24b + 8 Directions: For questions 25 through 28, identify if inductive or deductive reasoning is being used. 25) Michelle has a stuffy nose, a sore throat, and a headache. She concludes that she has a cold. 26) In all of Bob s classes he has taken in high school, he has been given exams. He concludes that he will take exams in all of his college courses too. 27) Matt noticed that each of the four times he had a math test and he scored a good grade, he also ate a hamburger on the same day. He concludes that he should eat a hamburger on every day he has a math test so that he will get a good grade. 28) All numbers ending in a 0 or a 5 are evenly divisible by is a number that ends in a 5, so it is evenly divisible by 5.

4 Target 4: Use properties of equality and congruence to prove relationships Directions: Use the diagram to answer questions 29 through ) Find x. 31) Find y. 29) a) Name a pair of vertical angles. 32) What is the m BOF? b) Name a pair of complementary angles. 33) Which angles are complementary with CXB? 34) Which angles are supplementary to angle 1? 35) 1and 2 are vertical angles. 3 forms a linear pair with 2. 4 forms a linear pair with 1. What must be true? 36)AB CD and they intersect at point M. What must be true about the angles formed? Select all that apply. (a) 4 = 90 (b) 3 forms a linear pair with 1 (c) 4 3 (d) 4 2 (e) 3 forms a linear pair with 4 Select all that apply. (a) AMB is a straight angle (b) AMB is an obtuse angle (c) AMC forms a linear pair with BMC (d) AMD is complementary to DMB (e) AMD is supplementary to AMC

5 Free Response Directions: Complete the following proofs. 37) Given: 2 11(m 2) = 4(3m 4) Prove: m = 4 (1) (1) (2) (2) (3) (3) (4) (4) (5) (5) 38) Given: lines l and k are perpendicular, 2 and 3 are complementary Prove: 1 = (1) lines l and k are perpendicular (1) (2) 2 and 3 are complementary (2) (3) 1 is a right angle (3) (4) (4) Definition of a right angle (5) (5) Definition of complementary angles (6) 1 = (6) 39) Given: m AOB = 35, m AOC = 145 Prove: 1 and 2 are supplementary (1) m 1 = 35 (1) (2) m 2 = 145 (2) (3) AOB + AOC = BOC (3) (4) = BOC (4) (5) 180 = BOC (5) (6) AOB + AOC = 180 (6) (7) 1 and 2 are supplementary (7)