Geometry 1-#8 Ch. 1 Review Name: ____________________________ Period: ____ Sept 9. 10 2014 1. Vocabulary: Be able to define or describe each term. Which are the “building blocks of geometry?” Point – Line – Plane – Ray – Segment – Collinear points – Coplanar points – Congruent – Acute angle – Supplementary angles – Complementary angles – Obtuse angle – Right angle – Perpendicular Lines – Angle- 2. Postulates: The intersection of two lines is __________ The intersection of two planes is ____________ Through two points there is __________________. Through three non-collinear points there is ______________________. If point R is between points P and Q on a line, then _________________________________ If point S is in the interior of PQR, then _________________________________ * Draw figures for the last two postulates. 3. Lines, Segments, Rays, and Angles a) Name the line four different b) Draw AB ways. A C B c) Draw AB m d) Draw PQR with a protractor such that mPQR 20 e) Draw three collinear points A, B, and C. f) Name the plane two different ways. Q A B C D 4. Circle the statements that are true and use correct notation for each diagram. Cross out the incorrect statements. Make sure you understand the difference between = & , AB & AB , and mABC & ABC . a) b) F A 12 cm B A 27° B C D AB CD , AB CD , AB CD , AB 12 cm, CD 12 cm D C mFDE 27 mFED 27 mFED mABC ABC 27 mFED mABC E mABC 27 FED ABC 5. Use the figure to answer the questions. a) ____________ = 30° A C 60 70 80 7 0 60 13 c) mEBD mDBC m __ __ __ 0 50 D d) mABD _____° 20 160 0 6. Planes a) Name plane that represents the top of the box. b) Name the intersection plane SVW and plane STX. e) mABE _____° 170 180 10 10 0 180 170 20 B 160 15 0 0 30 F 12 0 15 14 0 2 0 1 13 b) __________ ____________ 100 1 10 40 30 0 10 10 01 90 0 14 40 50 80 E f) __________ & ___________ are supplementary angles. d) Name the intersection plane VUY , plane TUX, and plane SVT. e) Name the planes whose intersection is ZY . c) Name another point on plane SWX. 7. Point R is between T and V on TV . Sketch a figure for each problem. a) TR = 15 cm, TV = 47 cm. Find RV. 5 3 b) TR = in, RV = in. Find TV. 8 5 (no calculators, show work with fractions) 8. Novato is between San Rafael and Ronhert Park along a straight highway. The distance from San Rafael to Rohnert Park is 50 miles. The distance from Novato to Rohnert Park is 2 miles more than 5 times the distance from San Rafael to Novato. Find the distance from Novato to Rohnert Park and from Novato to San Rafael. Show a diagram. Show work with an equation. 9. Use the figure on the right to… a) Name a right angle. d) Name a supplement of DOE. e) Name two angles that are complementary. b) Name an acute angle. c) Name an obtuse angle. f) Name two segments that are perpendicular. 10. Draw an angle that has a measure of 125° with a protractor. 11. Use a protractor to measure 1 and 2. 2 12. Angle addition postulate a) mCSE 55, mESL 12, mCSL ______ 1 13. mCSE 3( x 2), mESL 8( x 3), mCSL 74 Find the value of x and mCSE and mESL . b) mCSE _____, mESL 48, mCSL 87 L E L E S C S C 14. translate the figure along the line. Use the appropriate prime notation to label the image. 15. reflect the figure over the line. Use the appropriate prime notation to label the image. C C A B A B 16. rotate the figure around the point. Use the appropriate prime notation to label the image. 17. Name each type of transformation (choices: reflection, rotation, translation) a. C Pre-image Image B A b. Pre-image 18. Transform the triangle from (x,y) to (x + 7, y) 19. If triangle ABC is rotated 180° about the origin which of the following are the coordinates of B ' . B Describe the transformation in words: C B Image A C A A (4,–3) 20. Reflect the triangle across the x-axis. Write the rule: (x,y) to ( , ) B (–4,–3) C (–3,–4) D (3,–4) 21. Describe in words the result of applying each rule. a) (x,y) to ( x 3, y ) b) (x,y) to ( x 1, y 2) C B A c) (x,y) to ( x, y ) 22. Write the rule for each description. a) translate 4 units up b) reflect over y-axis c) translate 2 units left 23. The vertices of ABC are A(3, –1) , B(3, 4), and C(0, 1). If ABC is translated 2 units down and 3 units to the right to create DEF, what are the coordinates of the vertices of DEF. A D(6,–3) E(6, 2) F(3,–1) B D(1,2) E(1, 7) F(–2,4) C D(6,–4) E(6, 1) F(3,0) D D(5,–3) E(5, 2) F(2,–1) 24. Which expression describes the translation of a point from (5, –2) to (8,–6)? A B C D 3 units left and 4 units up 3 units right and 4 units up 3 units left and 4 units down 3 units right and 4 units down 25. Let point A be (2, - 4) and point B be (-8, 1). (work space) a. Find the slope of segment AB b. Find the distance from point A to point B c. Find the coordinates of the midpoint of AB d. Write the equation of the line that contains points A and B e. Write the equation of the line that is perpendicular to line AB and contains the point (1, 6) Some final notes: Look at the answers below- remember to mark any questions that you can not correct on your own. We’ll go over those in class before the test on Th/Friday. For the test, you may use your green sheet of notes and a protractor, but nothing else. (no calculator, no old homeworks.) I will be collecting your binder and grading it while you are taking the test- I’ll be looking at all HW from Ch 1, as well as your 3 dividers (notes, quizzes/tests, homework/classwork.) You will get 5 points for having an organized binder in class on the test day, plus I’ll record your Ch 1 HW completion score. ANSWERS: 1. * means “building block of Geometry” *Point – no dimension, named with capital letter *Line – extends infinitely in 2 directions, named with 2 capital letters with arrows above *Plane – flat, extends infinitely in all directions, named with the word plane followed by 3 letters or a cursive capital letter Ray – part of a line with an endpoint and extends infinitely in one direction- named with endpoint first Segment – part of a line with two endpoints Collinear points – points on the same line Coplanar points –points in the same plane Congruent – same size, same shape Acute angle – angle measure less than 90 degrees Supplementary angles – two angles whose measure sums to 180 P Complementary angles – two angles whose measure sums to 90 Obtuse angle – angle measure more than 90, less than 180 degrees R P Q S Right angle – angle that measures 90 degrees Q Perpendicular Lines –two lines that intersect at a right angle Angle- two rays that share a common endpoint R 3. point, line, one line, plane, RP plus PQ = RQ , measure of angle PQS plus measure of angle SQR = measure of angle PQR, see drawings 3. AB, CB, BA, linem b. A B c. A B d. check with protractor e. A B C f. plane ABD, plane Q 4. correct: first, third, fourth b. correct: second, fifth, last 5. a. m<EBD or m<CBA , b. EBD CBA c. EBC d. 80 e. (many correct answers) <EBD and <DBF 6. plane SVT b. line SW c. T d. U e. plane VUY and plane WXZ 7. 32 cm b. 49/40 8. Nov to RP is 42 mi, SR to Nov is 8 mi. 9. a. <BOD or <BOA b. <DOC or <COB or < BOA c. angle EOB or angle AOC or angle DOE d. <EOA e. angles DOC and BOC f. segments AD and BO 10. Measure with protractor 11. 26 and 116 degrees 12. 67 degrees, b. 39 degrees 13. X = 4, m<CSE = 18 degrees, m<ESL = 56 degrees 14-16 see tracing paper 17. a. reflection b. translation 18. Shift 7 to the right, A’ = (3, 1) B’ = (6, 3) C’ = (2, 4) 19. B 20. (x, y) to (x, -y) , A ‘ = (-1, -1) B’ = (2, -3) C’ = (-2, -4) 21. a. shift 3 left b. shift one right, down two c. reflect across both axes OR 180 degree rotation 22. (x, y) to (x, y+4) b. (x, y) to (-x, y) c. (x, y) to (x-2, y) 23. A 24. D 25. a. -1/2 b. √125 c. (-3, -3/2) d. y = -1/2 x -3 e. y = 2x + 4