Geometry: CBA-I Review

Transcription

1 Name: Period: ate: Geometry: I Review 1. Identify each construction. X Identify the converse, inverse, contrapositive, and bi-conditional form of the statement given below. If a triangle is equilateral, then it has three congruent sides. i-onditional: onditional: onverse: Inverse: ~ ~q ontrapositive: ~ ~ Switch Negate Switch & Negate Hint: Memorize this information. If a triangle is not equilateral, then it does not have three congruent sides. If a penguin has purple feathers, then it is not an equilateral triangle. triangle is equilateral if and only if it has three congruent sides. If a triangle has three congruent sides, then it is equilateral. If a triangle does not have three congruent sides, then it is not equilateral. Unit 1 Review Page 1

2 3. Name the intersection of: E Hint: Two Planes Intersect in Exactly One Line. F Plane & Plane EF: Plane EF & Plane : Plane EF & Plane EF: Plane & Plane : 4. The Smith and Wilson Families are staying at a campground. The Smiths leave camp and hike 6 km west and 5 km south. The Wilsons leave camp and hike 3 km east and 7 km north. How far apart are the families? Round your answer to the nearest tenth. Hint: Start at the origin and map each route to find the coordinates of the location of each camp. Then use the distance formula to find how far apart the Smith and Wilson Families are. =( ) +( ) N W E S Unit 1 Review Page 2

3 5. Given (-5, 7), & (4, -3). Given X(2, -9), & Y(-6, 6) Find Find the midpoint of Find XY Find the midpoint of XY 6. Given: l m. Find the measure of 5. (2(7x + 4)) l (5(4x + 14)) 5 m m 5 = 7. In T, = 12, T = 15, and T = 17. List the angles of T in order from smallest to largest? In OG, m = 100, m O = 37, and m G = 43. List the sides of OG in order from shortest to longest? Unit 1 Review Page 3

4 8. Match the following Terms & efinitions: (Use Each nswer Only Once.) onjecture ounterexample oplanar Lines Parallel Lines Intersecting Lines Perpendicular Lines Non-oplanar Lines Skew Lines. Lines that are not contained in the same plane.. statement that one thinks may be true.. oplanar Lines that intersect to form four right angles.. Non-coplanar Lines that are not parallel and do not intersect. E. statement that proves that a conjecture is false. F. Lines that are contained in the same plane. G. oplanar Lines that are not parallel. H. oplanar Lines that do not intersect. 9. Identify a counterexample for the conjecture below. Hint: Find the hypothesis (p) and the conclusion (q). For a counterexample p must be true and q must be false. Juanito has 25 cents in his piggy bank so he must have 4 coins or less.. Juanito has a quarter.. Juanito has 2 dimes.. Juanito has 1 dime and 3 nickels. Juanito has 5 nickels. 10. In the figure shown below, and X X. What triangle congruence postulate would prove that X X?. SSS. S E. SS G. HL. SS. S F. HL H. lternate Interior s Unit 1 Review Page 4

5 11. Find the m if bisects and the m = (2x + 7) and m = (6x 9).. =4. =45. =15. = Find the m if bisects and the m = (3x + 8) and m = (8x 24).. =19.2. =68. =136. = eto is trying really hard to prove that IK OMG. Which sets of congruencies are not valid ways to prove the two triangles congruent? I. I O, M, & K MG. I O, IK OG, & K G. I O, M, & K G. I OM, K MG, & GO KI E. K MG, I O, & KI GO F. K MG, KI GO, & K G K G O M Unit 1 Review Page 5

6 14. Given Equilateral Triangle, identify the answer which gives a possible algebraic measurement for the third side. (12x 21) (7x + 4). =8x. =12x 27. =6x+2. =9x Identify the correct triangle congruence theorem or postulate for each set of given information: If:, E Then: E by Note: The ase ngles of an Isosceles Triangle are ongruent. If:, & E Then: E by If: E, X X Then: EX X by 16. List all valid conclusions which may be deduced from the figure below: 40 Unit 1 Review Page 6

7 17. Identify the triangle congruence postulate or theorem that can be used to prove the following pairs of triangles are congruent: 18. Given the line determined by the equation 3x 4y = 24. Write the equation, in slope - intercept form, of the line perpendicular to it which passes through the point (6, -2). Note: Use the graph below to check your work. Unit 1 Review Page 7

8 19. Given graphed below, passing through the points (-6, -4)& (3, 2); give the equation for the line parallel to and passing through the point X(-3, 4) in slope-intercept form. Hint: Find the slope, then write the equation in point-slope form, then convert to slope-intercept form. heck: Graph your line and plot point X. id your line hit point X?. = +4. = 2. = +6. = Given, with vertices at (1, 5), (7, -3),& (-5, -1); give the equation for the perpendicular bisector of in standard form. Hint: Find the midpoint of. Then find the slope of. Then give the slope perpendicular to. Using this slope and the midpoint of, write the equation in point-slope form, graph to check, then convert to standard form. heck: Is your line to at its midpoint?. 3+4= =8. 4 3= = 8 Unit 1 Review Page 8

9 21. Given the figure below, which postulate or theorem justifies each conclusion indicated. nswer ank: orresponding ngles Postulate lternate Interior ngles Theorem lternate Exterior ngles Theorem Same Side Interior ngles Theorem Same Side Exterior ngles Theorem = = Find the measure of Unit 1 Review Page 9

10 23. Let l be the Perpendicular isector of. Graph l and write its equation. Let m be the Perpendicular isector of. Graph m and write its equation. nswer the following questions. Equations: l : isector of m : isector of Mark several miscellaneous points on each bisector and list their coordinates: Points on l : Points on m : What will be the x coordinate of any point on l? _ What will be the y coordinate of any point on m? What then must the coordinates of their intersection be? 24. bisects. If =5+15 and =34 9,what is? Unit 1 Review Page 10

11 25. Identify the type of reasoning (Inductive / eductive) used in each of the following situations: Hints: Inductive Reasoning uses experiment, observation, and patterns in data to make conjectures. eductive Reasoning uses facts, definitions, and postulates to prove conjectures.. Francisca notices that the storm siren is tested every Wednesday around noon, so she was not afraid when it began sounding this Wednesday at 11:58.. eto read an announcement, on the Flat Screen in ommons, that there will be a Pep Rally this Friday, so he made sure that his 3 rd period teacher let him out for lunch on time.. Jasmine performed a mathematical experiment. She multiplied 12 pairs of odd numbers together. Each time the product was also an odd number. Jasmine conjectured that the product of two odd numbers will always be an odd number. 26. Mr. Newton drew the diagram below with 1 5 and 1+m 2 equal to Which of the following is a logical conclusion about his figure?. 4 5 are compelementary are supplementary In the figure below, O and XZ are right angles. The O=32x 8 and the ZXY=60. If the = XY, then what is the value of x? O X. 60 Z Y Unit 1 Review Page 11