Name. Period. Teacher

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1 Name Period Teacher

2 MONY TUESY WENESY THURSY FRIY ug st day Welcome ourse Syllabus alendar Start Powers egin Vocabulary 1 st Six Weeks Geometry PP 1.1 Identifying points, lines, and planes Give Picture conclusions Wksht 1.1 all More 1.1 Identifying points, lines, and planes More 1.1 Identifying points, lines and planes 31 Sept Use Segments and ongruence 1-2 ay 2 Use Midpoint and istance Formula 1-3 Measure and classify angles Summer packet quiz, WU1 1-4 escribing angle pair relationships Quiz #1 WU2 Hw: 1-4 escribing angle pair relationships Quiz #1 WU2 Hw: Short flow proofs Review WU Holiday Test #1 2-5 algebraic proofs Powers quiz 2-5 algebraic proofs Powers quiz 2-2 nalyzing onditional Statements eductive Reasoning ay 2 2.5/2.6 proofs with segments, angles, and angle pairs Review Review Test # /4/6 25 1/3/5/7 3-1 Lines and ngles 3-2 Properties of Parallel lines WU1 Holiday 3-3 Parallel line proofs ay 1 WU2 3-3 Parallel line proofs ay 1 WU Oct. 1 2 Review WU3 School pics Test #3 3-7 Equations of lines in a coordinate plane 3-7 Equations of lines in a coordinate plane 3-8 Slopes of Parallel and Perpendicular lines ll answer keys can be found on Mr. Schroeder s/ms. Zita s Website, students are responsible for checking their work before the next class meeting. ll work must be shown and explanations given when stated in the problem, failure to do so will result in credit not being given for the assignment.

3 2-5 Using lgebraic Properties Name: Identify the property that justifies each statement If m 1 m 2, and m 2 m 4,then m 1 m If x y, then y x If ST YZ, and YZ PR,then ST PR If KL PR, then KL PR If b a and b 0, then a Figure Figure If m EF m, then m EF m GHI m m GHI 9. x y 10. If x y, then If, then. 11. x 12. If 7, then x If x 5 and b 5, then x b If XY WZ, then XY WZ If m m and m m, then m m If HJ 5 20, then HJ If XY 20 YW and XY 20 T, then YW T If m 1 m 2 90 and m 2 m 3, then m 1 m If 1 1 EF, then EF If 3 2 x 5 2, then 2x If m 4 35 and m 5 35, then m 4 m If 2 2, then If EF GH and GH JK, then EF JK 23. Give the reason for each step 24. 8x x 40 x 5 x x x 15 4x 8 x 15 8 x 23

4 Use the property to complete the statement. 26. Reflexive Property: SE 27. Symmetric Property: If, then m RST m JKL 28. Transitive Property: If m F m J and, then m F m L. 29. ddition Property: If RS TU, then RS Multiplication Property: m 1 m 2, the 3 m Substitution Property: If a 20, then 5a Reflexive Property If x is a real number, then x. 33. Symmetric Property: If, then. 34. Transitive Property: If m E m F and m F m G, then. 35. Multiplication Property: If RS TU, then x RS. 36. ivision Property: If 3 m 1 3 m 2, then m Transitive Property: If a bc and bc de, then. 38. Substitution Property: If x 3c and r 5x 7, then. Give the reason for each step 39. 4x 7 6x x 7 7 2x 14 x 7 1 x y x 9 y 7 7x 63 y y 7x 63 Solve each equation. Give a reason for each step x 11 4x x 3 19x x x x

5 Worksheet 2-2 onditional Statements PP Rewrite the conditional statement in if-then form. 1. car with leaking antifreeze has a problem 2. on t say anything at all when you don t have something nice to say. 3. You can t teach an old dog new tricks. 4. vein is a blood vessel that carries blood toward the heart. 5. It is time for dinner if it is 6 P.M. 6. n obtuse angle is an angle that measures more than 90 and less than 180 Write the converse, inverse, and contrapositive of each statement. (for #9-10 write the if-then also.) 7. If you like football, then you go to the football game. 8. If x is odd, then 3x is odd. 9. circle with a radius of r has a circumference of 2 r. 10. ny two adjacent angles share a common side. Write the converse of each true statement. If the converse is also true, combine the statements to write a true biconditional statement. 11. If an angle measures 30, then it is acute. 12. If two angles are supplementary, then their sum is If two circles have the same diameter, then they have the same circumference. 14. If an animal is a panther, then it lives in the forest. In a plane, point F lies between points and and EF intersects so That FE FE. ecide whether the given statement is true. Explain your answer using definitions and properties that you have learned. (draw picture) 15. F and FE are opposite rays. 16. FE and FE are adjacent angles 17. F and EF are a linear pair. 18. FE and FE are a linear pair. 19. FE is an obtuse angle. 20. EF ecide whether the statement is true or false. If false, provide a counterexample. 21. The equation 4x x has exactly one solution. 22. If 2 x 36, then x must equal If an odd number is less than 10, then it is a prime number.

6 Practice with 2-4 eductive Reasoning Name etermine if statement (3) follows from statements (1) and (2) by either the Law of etachment or Law of Syllogism. If it does, state which law was used. If it does not, write invalid. 1. (1) If an angle measures more than 90, then it is not acute. (2) m 120. (3) is not acute. 2. (1) ll 45 angles are congruent. (2) (3) and are (1) If you order the apple pie, then it will be served with ice cream. (2) Matthew ordered the apple pie. (3) Matthew was served ice cream. 4. (1) If you wear the school colors, then you have school spirit. (2) If you have school spirit, then the team feels great. (3) If you wear the school colors, then the team will feel great. 5. (1) If you can eat too much turkey, then you will get sick. (2) Kinsley got sick. (3) Kinsley ate too much turkey. 6. (1) If 2 is acute, then 3 is obtuse. (2) If 3 is obtuse, then 4 is acute. (3) If 2 is acute, then 4 is acute. In problems 7-10, decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning. 7. ngela knows that Walt is taller than Peter. She also knows that Peter is taller than Natalie. ngela reasons that Walt is taller than Natalie. 8. Josh know that rand X computers cost less than rand Y computers. ll other brands that Josh knows of cost less than rand X. Josh reasons that rand Y cost more than all the other brands. 9. For the past three Wednesdays, the cafeteria has served macaroni and cheese for lunch. ana concludes that the cafeteria will serve macaroni and cheese for lunch this Wednesday. 10. If you live in Nevada and are between the ages of 16 and 18, then you must take driver s education to get your license. nthony lives in Nevada, is 16 years old, and has his driver s license. Therefore, nthony took driver s education.

7 Use law of detachment to make a valid conclusion in the situation. 11. If you get a hit, then your baseball team will win. You hit a home run. 12. If Rylee gets promoted, then allie will also be promoted. Rylee is promoted. 13. ny time Kendra runs in a cross country race, if she runs a strong race, then she wins. In the cross country race last Saturday, Kendra ran her best race. 14. If two integers are added together, then the result is an integer. You add an integer x to another integer y. 15. If you double a negative number, then the result is a smaller number. You calculate 2x, where x< If an integer is divided by one of its factors, then the result is another one of the integer s factors. You divide an even integer x by 2. Use the law of Syllogism to write the statement that follows from the pair of statements that are given. 17. If Moose is hungry when he goes to the pizza shop, then he ll finish a whole pizza. If Moose eats a whole pizza, then he goes through a pitcher of soda. 18. If you mail the payment by noon, then it will arrive by tomorrow. If you payment arrives by tomorrow, then you won t be charged a late fee. 19. If Estelle takes her broker s advice, she ll invest in stock X. If Estelle invests in stock X, she ll earn 50% on her investment by next year. 20. If a triangle has two angles of 60, then the triangle is equiangular. If a triangle is equiangular, then it is also equilateral. ecide whether the conclusion reached from the two statements demonstrates the Law of etachment, the Law of Syllogism, or neither. 21. If edric plays in a big game, then he gets nervous. If edric gets nervous, then he performs well. onclusion: If edric plays in a big game, then he performs well. 22. If Leanne spends more than $30 on her car, then she ll have to wait until next week to buy Michael s birthday gift. Leanna spent $40 on her car. onclusion: Leanne will have to wait until next week to buy Michael s birthday gift. 23. If Lavonne gets money, she gives half of it to Sid. If Sid gets money, he gives half of it to Lavonne. onclusion: Lavonne and Sid share their money equally.

8 eginning Proofs Give a flow proof for each. 1) Given: is between and Prove: 2) Given: is the midpoint of Prove: 3) Given: bisects Prove: 4) Given: Prove: m m m 5) Given: bisects Prove: 6) Given:, E EF Prove: EF E F

9 7) Given:, E Prove: E E 8) Given: E Prove: E E 9) Given: E Prove: E E 10) Given: Prove: 11) Given: Prove:

10 12) Given: Prove: m 1 m ) Given: 1 and 3 are vertical angles Prove: ) Given: 2 4 Prove: ) Given:, 1 4 Prove:

11 Worksheet 2-5 & 2-6 Segment and ngle Flow Proofs Part 1 Name 1) Given:, Prove: is the midpoint of Instructions: For 1-9 write the reason next to each box. is the midpoint of 2) Given: and E Prove: E E E E E E E E E 3) Given: is between and, is between and Prove: is between and is between and

12 4) Given: is the midpoint of Prove: is the midpoint of 5) Given: E, EF Prove: F E F E EF E EF F E EF E E EF F 6) Given: E Prove: E E F E E E E E E E E E

13 ) Given: E EF 8) Given: 1 2, 3 2 Prove: GE is a segment bisector Prove: 1 3 E F G E EF E is the midpoint of F 2 3 GE is a segment bisector 1 3 9) Given: M 5 and P 7 Prove: MP 12 M P MP M P M 5 P 7 MP 5 P MP 5 7 MP 12

14 10-12 onnect the statements with the base line, and give reason for each statement. 10) Given: O is the midpoint of, O O O Prove: O O O is the midpoint of O O O O O O O O O O 11) Given: m 1 m 2, m 3 m 4 Prove: m QPS m QRS P S Q R m QPS m 1 m 3 m 1 m 2 m 3 m 4 m QRS m 2 m 4 m QPS m 2 m 3 m QPS m 2 m 4 m QPS m QRS

15 12) Given: m FOX 70 and m XOG 40 Prove: FOG is obtuse F X O G m FOG m FOX m XOG m FOX 70 m XOG 40 m FOG 70 m XOG m FOG m FOG 110 FOG is obtuse. Solve the following problems. Work these problem on your own sheet of paper. 13) pair of vertical angles have the following measures, m 1 4x 50 m 2 2x 10. What is the value of x and the supplement of 2. and ) Two angles form a linear pair. m 3 2x 15 and m 4 3x 5 is the value of x and is 4 acute, right, obtuse?. What ) 5 is supplementary to 6 measures of the angles. 2. If m 5 x and m 6 8x, then find the 5 6

16 2 is bisected by ME. If m ME x 10 and m EMY 3x 30 16) MY then what is m MY?, E Y M Use the picture at the right for problems TMR is a right angle. 17) Name an angle supplementary to QMS. T Q 18) Name an angle complementary to QMS. 19) Name a pair of adjacent angles that do not form a straight line. R M S 20) Name a pair of adjacent angles that do form a straight line. 21) Name an angle that is complementary, but not adjacent, to TMQ. P 22) Name a pair of vertical angles. 23) Which angle forms a linear pair with PMR. 24) Two lines intersect to form vertical angles. If each of the angles formed are congruent, then what is the measure of the angles? 25) Two angles form a linear pair. If one angle is x and the other is 1 x 10, then find the angles? 2

17 Review for Test #2 PP Name Period Name the property, theorem, or postulate that justifies each statement. 1) TJ TJ. 1) 2) If 2 2WV, then WV. 2) 3) If XY and F MN, then F XY MN. 3) 4) T T. 4) 5) If PO WE and WE QR, then PO QR. 5) 6) If, then. 6) 7) PQ PQ. 7) 8) If 2m 180, then m 90. 8) 9) If m , then m ) 10) If 5 3x 4, then 3x ) 11) If 3 x 2 2, then 3x ) 12) If m 1 m 2 90 and m 2 m 3, then m 1 m ) Write a flow proof for 13-14: 13) Given: T is between Q and J. QT KJ Prove: KJ TJ QJ Q T J K 14) Given: M is the midpoint of YF F is the midpoint of M Prove: 3YM Y Y M F

18 Write a complete proof for the following. 15) If x 6, then x ) If 4 x 3 23, then 11 x 4 3 x ) If 3x 5 x 7, then 3 18) If, 4x 1, and 6x 13, then x 7 Write a flow proof for ) Given: R HK.. R K H Prove: RK H 20) Given: m SWR m HWF Prove: m SWF m RWH... S F R. W H 21) Given: line w bisects T. Prove: T. T. w 22) Given: P OP, G Prove: GP is a segment bisector. P O Solve the following. 23) 2 and 5 are vertical angles. If m 2 7x 2 and m 5 x 34 the value of x and the measure of 5., then find 2 5

19 24) WY bisects XWZ. If m YWZ 9x 10 and m XWY 2x 39, then find m XWZ. Y X Z W 25) 1 and 5 are complementary. 3 and 5 then what is the value of x and the measure of 5? are complementary. If m 1 2x 2 and m 3 x 32, ) 7, 8, and 9 together form a straight angle. If m 7 x 20, m 8 x 40 m 9 x 30, then what is the value of x and the measure of the three angles?, and ) 5 and 6 form vertical angles. If m 5 x and m 6 6x 290 of x and the measure of the angles., then find the value ) 1 and 2 form a linear pair. If m 1 2x 4 and m 2 2x 4 of x and the measure of the angles., then find the value 1 2 Write the conditional, converse, inverse, and contrapositive for the following statements. 29) omplementary angles add to 90 degrees. 30) If you like hockey, then you go to the hockey game.

20 etermine if statement (3) follows from statement (1) and (2) by either the Law of etachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. 31) (1) If an angle measures more than 90, then it is not acute. (2) m 120 (3) is not acute. 32) (1) If you eat too much turkey, then you will get sick. (2) Kinsley got sick. (3) Kinsley ate too much turkey. 33) (1) If you wear the school colors, then you have school spirit. (2) If you have school spirit, then the team feels great. (3) If you wear the school colors, then the team will feel great. For problems 34-35, Use the laws of logic to make a conclusion if possible. 34) If a rectangle has four equal side lengths, then it is a square. If a polygon is a square, then it is a regular polygon. 35) If the measure of an angle is 90, then it is a right angle. The measure of is 90 36) escribe and correct the error in the argument: If two angles are a linear pair, then they are supplementary. ngles and are supplementary, so the angels are a linear pair.

21 hapter 2 Overview PP 1) What is inductive reasoning? conjecture based on observations/patterns 2) What is a conjecture? n unproven statement 3) What is a counter example and what does it do? specific case for which a conjecture is false. 4) What is a conditional statement? What is the symbol for a conditional statement? logical statement with 2 parts, a hypothesis and a conclusion. It is usually written in if-then form. p q 5) What is if then form? form to write a conditional statement. 6) What is the hypothesis in an if-then statement? Everything after if in an if-then statement 7) What is the conclusion in an if-then statement? Everything after then in an if-then statement 8) What is a converse? What is the symbol for a converse statement? Is an exchanging of the hypothesis q p 9) What is negation? Opposite of the original statement 10) What is a inverse? What is the symbol for an inverse statement? negation of the conditional. p q 11) What is a contrapositive? What is the symbol for a contrapositive statement? negation of the converse. q p 12) How many statements use negation, and which are they? Two, inverse and contrapositive 13) efine perpendicular lines. It two lines intersect to form a right angle, then the lines are perpendicular. 14) What symbol determines perpendicular lines? box 15) What are equivalent statements? When 2 two statements are both true or false. onditional and ontrapositive should be both true or both false. The same for converse and inverse. 16) What is a biconditional statement? When a conditional and its converse are both true, the statement can be written as an if and only if statement. 17) What is deductive reasoning? Using facts, definitions, properties, and laws of logic to form a conjecture. 18) What is the Law of etachment? If hypothesis of a true conditional is true, then the conclusion is also true. 19) What is the Law of Syllogism? If hypothesis p, then conclusion q, If hypothesis q, then conclusion r. If hypothesis p, then conclusion r. 20) What are you looking for to know it is Law of etachment? very general statement to start, and a very specific hypothesis, so that you can make a very specific conclusion. 21) What are you looking for to know it is Law of Syllogism? The chain rule, a to b and b to c, then a to c. 22) How many point, line, and plane postulate are there? Seven

22 23) List the point line plane postulates Post 5 Through any two points there exists exactly one line. Post 6 line contains at least two points. Post 7 If two lines intersect, then their intersection is exactly one point. Post 8 Through any three noncollinear points there exists exactly one plane. Post 9 plane contains at least three noncollinaer points. Post 10 If two points lie in a plane, then the line containing them lies in the plane. Post 11 If two planes intersect, then their intersection is a line. 24) What are the 8 properties of equality? (Use examples) ddition Property Substitution Property Subtraction Property Transitive Property Multiplication Property Reflexive Property ivision Property Symmetric Preperty 25) What is the segment addition postulate? If is between and then +=. 26) What is the angle addition postulate? If P is in the interior of RST, then m RSP m PST m RST. 27) What is a linear pair? How do you set up a problem that has a linear pair? Two adjacent angles whose noncommon sides are opposite rays. ngle + ngle = ) What are supplementary angles? How do you set up a problem with supplementary angles? Two angles whose sum is 180 degrees. ngle + ngle = ) What are complementary angles? How do you set up a problem with complementary angles? Two angles whose sum is 90 degrees. ngle + ngle = 90 30) What are vertical angles? How do you set up a problem with vertical angles? Two angles formed by 2 pairs of opposite rays. ngle = ngle 31) Why are angles 1 and 2 not vertical angles? (last question on 2 nd test) ecause the angles are not formed by 2 pairs of opposite rays ) What is the setup for using an angle bisector to solve a problem? ngle = ngle 33) What is the definition of a midpoint? point that divides a segment into 2 congruent segments. 34) What is the definition of an angle bisector? ray that divides an angle into 2 congruent angles. 35) Find an equation that you solved from one of your old worksheets and list the reasons for each step of solving of that equation. 36) What is a segment bisector? What is the setup for using a segment bisector to solve a problem? point, line, plane that intersects that midpoint. Segment = Segment 37) What is the difference between a segment bisector and a midpoint? segment bisector tells you where a midpoint is, a midpoint divides a segment into 2 congruent parts. 38) o adjacent angles help solve a problem? Not necessarily. They could help with angles addition postulate. 39) Is there a special set up for adjacent angles? If so, what is it? No, trick question. 40) Why are pictures drawn in Geometry? So that the right parts are seen and the equations can be determined from the vocabulary.

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