Geometry Midyear Exam Review 2017

Transcription

1 Geometry Midyear Exam Review 201 From the Extra Practice section at the back of the book, these exercises will remind you of the topics studied. The problems start on page 818 and are referenced by Lesson sections. Lesson 1.1; All Lesson 4.1; All Lesson 1.2; #1-6 Lesson 4.2; All Lesson 1.3; #4-9 Lesson 4.3; All Lesson 1.4; #5- Lesson 4.4; All Lessons 1.5 & 1.6; Look at the problems to Lesson 4.5; #1-6 remember the terms and items for multiple Lesson 4.6; All choice or short answer type problems. Lesson 1.; All be able to list the coordinates of the points for #1-4 when original points are given. Lesson 2.2; All Lesson 2.3; Know how to do parts a, b, & c for any of #1-5. Lesson 2.4; All Lesson 2.5; All Lesson 5.1; #1, 3, 6, Lesson 5.2; #1-3, 4, 6, 8 Lesson 5.3; #1-4, 9, 10 Lesson 5.4; All Lesson 5.5; All Lesson 5.; #1- Lesson 5.8; #1-3 Lesson 3.2; All Lesson 3.3; All Lesson 3.4; #1-6 Lesson 3.5; All Lesson 3.6; All Lesson 3.; #1-5 Lesson 3.8; #1-8 Remember: Exam day/date: Time: Bring:

2 Key: GEOMETRY MIDTERM REVIEW ANSWERS pg Lesson 1.1 1) AB, BC, CD, DA 2) plane ABC (or BCD or ABD etc) 3) ie: A, AB, and AD 4) True; (Postulate; The intersection of 2 planes is a line) 5) False: two lines might not be coplanar they could be skew lines. 6) False: only collinear points are contained in one line. ) point X 8) ie: VXW; XV and XW Lesson 1.2 1) 5 2) 6 3) 8 4) 22 5) 29 6) 4 Lesson 1.3 1) 42 2) 99 3) 5 4) 55 5) 0 6) 125 ) x = 5.5, m WXZ = 35 8) 1.5 9) 52.5 Lesson 1.4 5) m ABC = 0 m DBC = 35 6) 55 ) 55 Lesson 1.6 ie: 1) The figure will flip across the reflection line. 3) The figure will turn 180 and look opposite at that point.

3 Lesson 1. 5) vertical shift DOWN 3 units 6) horizontal shift RIGHT 2 units ) reflection across the y-axis, and vertical shift DOWN 5 units 8) Reflection across the line y = x Lesson 2.2 1) If an animal lives in the Everglades, then it lives in Florida. 2) H: an animal lives in the Everglades C: it lives in Florida 3) 4) If an animal lives in Florida, then it lives in Animals in Florida the Everglades. Animals in Everglades 5) H: two angles are supplementary C: the sum of their measures is 180 Converse: If the sum of the measure of two angles is 180, then the angles are supplementary. Converse is true. 6) H: your transportation is a motorcycle C: you ride on two wheels Converse: If you ride on two wheels, then your transportation is a motorcycle. Converse is false you could be riding a bicycle. ) H: you live in Baltimore C: you live in Maryland Converse: If you live in Maryland, then you live in Baltimore. Converse is false you may live in Annapolis or Gaithersburg. 8) H: you have a rose C: you have a flower Converse: If you have a flower, then you have a rose. Converse is false you may have a daisy, or carnation, etc.

4 Lesson 2.3 #1 & 2 as examples 1) a. If a planet is Mercury, then it is the planet closest to our Sun. b. If a planet is the closest to our Sun, then it is Mercury. c. A planet is Mercury if and only if it is the closest to our Sun. d. Definition OK because the biconditional is true. 2) a. If a place is a school, then it is where kids learn mathematics. b. If kids are learning mathematics, then they are at school. c. A place is a school if and only if it is the place where kids learn mathematics. d. NOT a definition: Kids may also learn mathematics at work, home, etc. Lesson 2.4 1) Addition Property of Equality 2) Subtraction Property of Equality; Division Property of Equality 3) 35 4) x = Lesson 2.5 1) GBE 2) FBE 3) ABC 4) 55 5) m ABE = m CBD = 13 m ABC = m EBD = 43 6) Inductive Reasoning: argument is based on examining examples.it s a generalization. ) Deductive Reasoning: the argument is true for ALL multiples of 5 (therefore it is a proof). Lesson 3.1 1) ie 2) 3) B

5 Lesson 3.2 1) 5 2) 5 3) 3 4) 4 5) 106 6) 90 ) x = 2, diagonals are 6 8) True 9) False; rhombus may have interior angles other than 90 10) True Lesson 3.3 1) 2, 6, 2) 1, 5, 8 3) No; all angles were listed in exercises 1 & 2 4) m 1 = m 4 = m 8 = 40 m 2 = m 6 = m = 140 5) m 1 = m 4 = m 5 = m 8 = 80 m 2 = m 3 = m 6 = m = 100 6) 5 ) 0 8) 0 9) 0 10) 35 11) 35 Lesson 3.4 (Remember the difference between the Theorems and the Converses.) 1) Alternate Interior Angles Theorem 2) Corresponding Angles Postulate 3) Same-Side Interior Angles Theorem 4) Corresponding Angles Postulate 5) Alternate Interior Angles Theorem 6) Same-Side Interior Angles Theorem Lesson 3.5 1) 90 2) Does not exist 3) 48

6 4) m HLK = m KJG = 55 m KGJ = 105 m HKJ = 160 m LKH = 20 m LHK = 105 5) 55 6) 5 ) 6 Lesson 3.6 1) 50 2) 130 3) 150 4) 5 5) 15 6) 9 ) 5 8) 8 9) 12 10) x = 54, so m F = 108, m G = 54, m H = 0, m I = 128 Lesson 3. 1) 30 2) 35 3) 45 4) 3 feet 5) 1.5 feet Lesson 3.8 1) m = ½ (2, 1.5) 2) m = ½ (0, 2) 3) m = (.5, 1.5) 4) m = 1 (1.5, -2.5) 3 5) Perpendicular 6) Perpendicular ) Neither 8) Parallel 9) Right triangle 10) NOT a right triangle 11) NOT a right triangle 12) Right triangle Lesson 4.1 1) Not congruent; different lengths 2) Congruent; same angle measures 3) Not congruent; different side lengths 4) Congruent; all corresponding parts are congruent

7 5) Congruent; all corresponding parts 6) Not congruent: corresponding are congruent angles are not congruent ) a) JM b) WC c) BA d) OP 8) L A, K E, J F, M X, N W, O C, P B Lesson 4.2 1) SSS 2) cannot be proven 3) ASA 4) Yes, SAS 5) NO 6) Yes, ASA ) No 8) Yes, SSS 9) Yes, ASA Lesson 4.3 1) ΔCMQ ΔFDB by SSS 2) NO 3) ΔABD ΔCBD by SAS 4) ΔABC ΔPQR by ASA 5) ΔRST ΔJKL by SAS 6) ΔWXY ΔERG by ASA or AAS ) NO 8) NO 9) ΔMNO ΔGHI by SSS 10) ΔRVU ΔOLP by AAS or ASA Lesson 4.4 1) 40 2) 85 3) 12 4) 150 5) 50 6) 5 ) 90 8) 13 9) 15 10) 23 Lesson 4.5 1) 150 2) 3 3) 40 4) 21 5) Lesson 4.6 1) Parallelogram; diagonals bisect each other 2) Parallelogram; one pair of opposite sides parallel and congruent

8 3) Parallelogram; two pairs of opposite sides congruent 4) NOT a parallelogram 5) Rhombus; diagonals of a parallelogram bisect the interior angles 6) Rectangle; diagonals of a parallelogram are congruent ) Rhombus; one pair of adjacent sides of a parallelogram congruent 8) Rectangle; one angle of a parallelogram is a right angle 9) Neither 10) Rhombus; diagonals of a parallelogram are perpendicular Lesson 4.8 4) Not possible; ) Possible; > > 1 and > 14 6) Possible; > 5 ) Not possible; > 3 and > 4 8) Possible; > 24 9) Not possible; > 20 and > 14 Lesson 5.1 1) 12 2) 20 3) 4 4) 18 5) 15 6) h = 14 in, b = in, A = 98 in 2 ) h = 3 cm, b = 12 cm, P = 30 cm 8) h = 16x, b = 4x, P = 40x Lesson 5.2 (all area is in square units) 1) A = 24 2) A = 1 ½ 3) A = 3.5 4) A = 15 5) A = 4 6) A = 80 ) A = 12 8) A = 15 9) A = 18 10) A = 16 11) A = 15

9 Lesson 5.3 (all area is in square units) 1) C = 18.8 A = ) C = 50.2 A = ) C= 44.0 A = ) C = A = 1,01.4 5) C = 880 A = ) C = 04 A = 5632 ) C = 528 A = ) C = 330 A = ) r = ) r = ) r = ) r = 1 13) r = ) r = Lesson 5.4 (all area is in square units) 1) 13 2) 130 3) ) 8 5) Obtuse 6) Right ) Acute 8) Right 9) Obtuse 10) Acute 11) A = 10.8 P = 15 12) A = 150 P = ) A = 1.1 P = 24.4 Lesson 5.5 (all area is in square units) 1) b = 3 c = 14 2) a = 3 c = 2 3 3) a = 2 b = 2 3 4) a = 6 b = 12

10 5) A = P = 66 6) A = 18 P = 12 3 ) A = 32 3 P = ) A = P = 60 9) A = 4.5 P = ) A = P = 48 Lesson 5. 1) C (b, a) 2) E (c, b) G (a c, 0) 3) b 4) c 5) b c 6) b 2 + c ) b 2 + c 2 Lesson 5.8 1) P = 8/25 =.32 = 32 % 2) P = ½ =.5 = 50% 3) P = 1/9 =.111 = 11.1%