REVIEW PACKET January 2012

Transcription

1 NME: REVIEW PKET January 2012 My PERIOD DTE of my EXM TIME of my EXM **THERE RE 10 PROBLEMS IN THIS REVIEW PKET THT RE IDENTIL TO 10 OF THE PROBLEMS ON THE MIDTERM EXM!!!** Your exam is on hapters 1 6 and Irregular rea. Don t forget to study hapter 6 (it is not in this packet, but will be covered on the exam!) NOTE: For additional preparation go to classzone.com or your textbook pp nswers to odd problems are in the back of the book. 1

2 Geometry Midterm Exam Formula Sheet (you will also get a copy of the Reasons List) y=mx+b y - y m = x - x x + x y + y (x,y) =, 2 2 d = (x x ) + (y y ) a + b = c = l w P = 2l + 2 w = 1 bh 2 P = a + b + c = πr 2 = πd = s 2 = b h 1 = d d = (b + b )h B I + U 2 2

3 hapter 1 1. Predict the next number in the sequence and describe the pattern. 5, 7, 10, 14, 19, 2. Draw a diagram illustration the following conjecture. Then draw a counterexample diagram showing the conjecture is not true. If WX and XY are congruent, then X is the midpoint of WY. 3. Based on the figure decide if the statements are true or false. a. Point W, lies on ZY X W b. Point X, W, and Z are coplanar. c. Point V, Y, and W are collinear. Y d. YV and YZ are opposite rays. V Z e. YV and YW are opposite rays. 4. Name a point that is coplanar with the given points. O S P, Q and S P N Q R M T 3

4 5. In the figure at the right, N is the midpoint of RT. If RN = 20 3x and NT = x + 4, then RT = R N T. 16 B D In the figure at the right, BD, B = 3x, B = 6x 5, and D = x + 6. Find the length of D. 3 B D Use the distance formula to find the distance between the points (-1, 0) and (2, -2). Equation: Solution: exact answer and nearest tenth 8. Use the ngle ddition Postulate to find the measure of the unknown angle. m B = D If PT B bisects RPS and m RPT = 3x + 13 and m TPS = 5x + 7, find the value of x. R Equation: T P S Solution: x = 4

5 10. Use the figure at the right to determine if the statements are true. a. 1 and 2 are adjacent b. 1 and 2 are a linear pair. c. 3 and are a linear pair d. 2 and 5 are vertical angles. e. 1 and 4 are vertical angles. 11. Find the measure of the angles using the figure at the right. a. If m 6 = 78, then m 7 =. 6 b. If m 8 = 94, then m 6 = Find the value of x using the figure below. Equation: 5x + 28 Solution: x = 12x Given points G (2, 10) and H ( -6, -10). Find the coordinates of the midpoint of GH Solution: 5

6 14. Find the value of x using the figure below. Then use that value to find the measure of B and BD. (2x + 8) (3x + 17) B D E 15. Find the perimeter (or circumference) and area of each figure below. ircumference: Equation: 10 ft Solution: = exact answer = nearest tenth rea: Equation: Solution: = exact answer = nearest tenth Perimeter: Equation 10 in. Solution: P = exact answer P = nearest tenth 20 in. rea: Equation: Solution: = 6

7 hapter 2 1. Write the converse, inverse, and contrapositive of the following conditional. If you like football, then you like to watch the Super Bowl. onverse: Inverse: ontrapositive: 2. Decide whether the following statement is true or false. If it is false, then give a counterexample. Through any three points there exists exactly one line. 3. Rewrite the following biconditional statement as a conditional statement and its converse. You may go to the movies Friday night if and only if you clean your room. onditional: onverse: 7

8 4. Using p and q below, write the symbolic statement in words. p: Drops of water are falling from the sky. q: It is raining a. p b. q p c. q p d. If q p is true and p q is true, what do you know about the biconditional q p? 5. Match the statement with the property of congruence or postulate. 1). If D PM and PM RV,then D RV. Symmetric prop. of seg. congruence. 2). B. Transitive prop. of seg. congruence 3). If R DB,then DB R. Segment ddition Postulate 4). If PQ+QR=30 and QR=10, then D. Reflexive prop. of angle congruence PQ+10=30 5). If B is between and, then E. Substitution prop. of equality B + B = 6. Write a two column proof. Given: 2 3 Prove:

9 hapter 3 1. Think of each segment in the diagram as part of a line. Fill in the blanks with parallel, skew, or perpendicular. a. B and D are b. B and B are c. BF and FG are d. B and FG are D E B F G 2. omplete the statements with corresponding, alternate interior, alternate exterior, or consecutive interior. a. 3 and 7 are angles b. 4 and 10 are angles c. 5 and 8 are angles d. 8 and 6 are angles Sate the reason for each conclusion. a. Given: m 1 = m 2 onclusion: 1 2 Reason: 1 2 b. Given: 3 and 4 are a linear pair onclusion: 3 and 4 are supplementary Reason: 3 4 c. Given: 5 6 onclusion: Reason: 9

10 4. Find the values of x and y. a. b. 70 x y y x In the figure k // m. If m 2 = 6x 24 and m 6 = 2x + 40, find m 4 and m 5. k Equation: m m 4 : m 5 : 6. Given: 1 2 Prove: m // n 1 n 2 3 m 10

11 7. Find the measures of the five numbered angles. m 1 = m 2 = m 3 = m 4 = m 5 = 8. The lines with equations y = 6x + 1 and 1 y = x are a. parallel b. perpendicular c. neither parallel nor perpendicular d. can t tell 9. Find the slope of each line. re the lines parallel? a. b. Show work using the slope formula. a. m 1 = b. m 1 = m 2 = re they parallel? m 2 = re they parallel? 11

12 10. What is the slope of the line that passes through the points (-1, 10) and ( 3, 2). Equation: m = 11. Write an equation of a line that passes through point (4, 6) and has a slope of 3 4. Equation: 12. For each equation below, a) write an equation parallel to the given line b) write an equation perpendicular to the given line I) y = 2x 4 II) + = 1 y 2 x Write the equation of the line perpendicular to a line with the equation y = x and passes through point (0, 5) Equation: 12

13 hapter 4 1. lassify each triangle by its angles and by its sides Is this an isosceles? 2. Find the measure of the numbered angles a. b

14 3. The variable expressions represent the angle measures of a triangle. Find the measure of each angle. m = (6x + 11) m B = (3x + 2) m = (5x 1) Equation: x = 4. In the diagram TJM PHS. omplete the statements below. P JM m M = m P = J S 5cm P 48 MT= TJ T 73 M H 5. Given: B DEF, find the values of x and y. B E (5x +2) D 3y F 14

15 6. a) If the triangles can be proved congruent, name the method (SSS, SS, S, S, HL). If they cannot be proved congruent, write none b) If the triangles are congruent, write the appropriate congruence statement. B B D D E a) b) B a) b) B R P B Q B a) b) B a) b) B For questions 7 9, write two column proofs. 7. Given: MQ NP,MP PQ,NQ PQ Prove: MPQ NQP M N O P Q 15

16 8. Given: B D,B D Prove: B D B D 9. Given: L //SN,LR NR Prove: LR NSR L S R N 10. onsider the two triangles shown. I G K L J H a. What theorem proves that the two triangles are congruent? b. IG c. GHI 16

17 11. Solve for x. (3x + 8) B x = Name the vertex angle: (2x + 20) Name the base angles: and 12. In the diagram below, if m T = 35 then m = T a. 70 b. 110 c. 155 d Solve for x and y. 3y (x - 2) (4x + 10) 17

18 hapter 5 1. In the figure below, points F and G are on the angle bisector of DE. The m BF = 54, F =16, DG = 20. Find: m F = B GE = D F E FB = G 2. In the figure is a perpendicular bisector of BD. Point E is on. EB = 10, B = 21. B Find: D = E ED = D 3. ccording to the Perpendicular Bisector Theorem, if P is on the perpendicular bisector of XY, then a. PX = XY b. PY = XY c. PX = PY d. None of these 4. Match the special segments (median, altitude, perpendicular bisector, angle bisector) with the figures below based on the markings. 18

19 5. Points R, T, and S are the midpoints of JKL. RK = 3, KS = 4. RS // J ST // JK = R T TS = 3 RT = K 4 S L Perimeter of JKL = 6. Points X, Y, and Z are the midpoints of the sides of MNO. If YZ = 3x + 1, and MN = 10x - 6, find the following: X = M YZ = Z X O Y N 7. List the sides of the triangles in order from smallest to largest. 61 D E 48 F 19

20 8. List the angles of the triangle from smallest to largest. L 9 8 K 10 M 9. triangle has sides of 4 and 11 units. What is the range of possible values for the third side? < x < 10. Fill in the blanks with <, >, or =. a. TU RS b. m 1 m 2 V 111 T R U B has vertices = (0, 4), B = (8, 6), and = (4, 0). a. alculate the midpoint of B. Graph it and label it P. P = ( ) b. alculate the midpoint of B. Graph it and label it Q. Q S B B Q = ( ) c. Verify PQ // d. Verify PQ is 1 2 the length of. 20

21 onstructions 1. Use a ruler to measure the given segment to the nearest tenth of a centimeter. 2. Use a protractor to measure the given angle to the nearest degree. 3. Use a ruler and a protractor to construct the perpendicular bisector to the given segment. 4. onstruct all of the medians of the given triangle. 5. onstruct all of the altitudes of the given triangle. 21

22 Irregular rea 1. Find the area of the irregular shape below. The side length of each square is 4 meters. I = B = U = 2. Find the area of Lake Millinocket. The side length of each square is 2 miles. I = B = U = 22