optional take home 3

Name___________________________________________ GEOMETRY TAKE HOME 3**SCANTRON AND PRINTED PACKET ARE DUE BEFORE FIRST PERIODON FRIDAY, JANUARY 4, 2013****NO TAKE HOMES WILL BE ACCEPTED AFTER FIRST PERIOD!****SHOW ALL WORK**1) In the diagram below of , .Using this information, it could be proven that1) 3)2) 4)2) When writing a geometric proof, which angle relationship could be used alone to justify that two anglesare congruent?1)supplementary angles2)linear pair of angles3)adjacent angles4)vertical angles3) In with shown in the diagram on the right, and are drawn.If, which statement could always be proven?1) 3)2) 4)4) In the diagram on the right of and , andintersect at E, such that and .Triangle DAE can be proved congruent to triangle BCE by1) ASA 3) SAS2) HL 4) SSS5) In the diagram of and on the right, AB DE , CB FE , and CA FD .Which method can be used to prove ?1) SSS 3) ASA2) SAS 4) HL

6) As shown in the diagram on the right, bisects and AB AD .Which method could be used to prove ?1) SSS 3) SAS2) AAA 4) AAS7) In the accompanying diagram, AB and CD intersect at E, E is the midpoint of DC, and A B .Which statement can be used to prove that ADE BCE ?1) ASA 3) SSS2) AAS 4) SAS8) If , which statement is always true?1) 3)2) 4)9) The diagram on the right shows a pair of congruent triangles,with and .Which statement must be true?1) 3)2) 4)10) In the diagram on the right, .Which statement must be true?1) 3)2) 4)11) In the diagram on the right, . Which two statementsidentify corresponding congruent parts for these triangles?1) 3)2) 4)

12) In the diagram on the right of and , , and .To prove that and are congruent by SAS,what other information is needed?1) 3)2) 4)13) If the measures of three angles of a triangle are represented by (y + 30)°,(4y + 30)°, and (10y – 30)°, then the triangle must be:1) obtuse 2) isosceles 3) scalene 4) right14) Which equation represents a circle with center (1,–3) and radius 4?1) (x - 1) 2 + (y + 3) 2 = 16 3) (x + 1) 2 + (y – 3) 2 = 162) (x - 1) 2 + (y + 3) 2 = 4 4) (x + 1) 2 + (y - 3) 2 = 415) Which equation represents circle K shown in the graph below?1)2)3(4)16) The center and radius of the given circle are:1) 3)2) 4)17) Which statement describes a circle with the equation (x + 4) 2 + (y - 6) 2 = 64 ?1) The center is at (-4,6) and the radius is 64.2) The center is at (4,-6) and the radius is 64.3) The center is at (4,-6) and the radius is 8.4) The center is at (-4,6) and the radius is 8.

18) What are the center and the radius of the circle whose equation is ?1) center = ; radius = 6 3) center = ; radius = 362) center = ; radius = 6 4) center = ; radius = 3619) The equation of a circle is . What are the center and radius of the circle?1) center = ; radius = 4 3) center = ; radius = 42) center = ; radius = 16 4) center = ; radius = 120) The new corporate logo created by the design engineers at Magic Motorsis shown in the accompanying diagram. If chords and are congruentand , what is ?1) 40 3)1402) 80 4) 28021) In the diagram on the right, circle O has . What is ?1) z 3)2) 2z 4)22) In the diagram on the right of circle O, chords and intersect at point B,such that and .What is ?1) 56 3) 282) 36 4) 823) In the diagram on the right, chords and intersect at E. If ,, and , what is the value of x?1)12 3) 302) 20 4) 6024) In the accompanying diagram of circle O, and . What is the measure of ?1) 104 3) 802) 52 4) 40

25) In the accompanying diagram, tangent and secant are drawn to circle O.If is twice and is 50, what is ?1) 25 3) 1002) 50 4) 20026) In the diagram below of circle C, , and . What is ?1) 50 3) 902) 60 4) 11027) The accompanying diagram shows two intersecting paths within a circular garden.What is the length of the portion of the path marked x?1) 3) 32) 11 4) 1228) In the diagram of circle O on the right, chord intersects chord at E, ,, , and . What is the value of x?1)1 3) 52) 3.6 4) 10.2529) In the diagram on the right, is a tangent to circle O at point S, is a secant,, , and . What is the length of ?1)6 3) 32) 9 4) 2730) In the diagram on the right, tangent and secant are drawn to circle O from external point P.If and , what is the length of ?1)20 3) 82) 9 4) 6

31) In circle O, the secant from S to D intersects the circle at C and the secantfrom S to B intersects the circle at A. If SC = 6, CD = 8 and SA = 4, find AB.1) 16/3 3) 212) 17 4) 28/332) In the diagram on the right of circle O, secant intersects circle O at D,secant intersects circle O at E, , , and .What is the length of ?1) 4.5 3) 92) 7 4) 1433) In the diagram on the right, is circumscribed about circle Oand the sides of are tangent to the circle at points D, E, and F.If , , and , what is the length of ?1) 8 3) 232) 15 4) 2734)In the diagram on the right, , , and are tangents to circle Oat points F, E, and D, respectively, , , and .What is the perimeter of ?1) 15 3) 252) 30 4) 6035) How many common tangent lines can be drawn to the twoexternally tangent circles shown below?1) 1 3) 32) 2 4) 436) In the accompanying diagram of right triangle ABC, altitude AD divides hypotenuse BC into segments withlengths of 4 and 5. Find the length of leg AB.1) 4.5 3) 62) 2.5 4) 7.5

37) In the diagram on the right of , D is the midpoint of ,O is the midpoint of , and G is the midpoint of .If , , and , what is the perimeter of parallelogram CDOG?1) 21 3) 322) 25 4) 4038) In ABC , DE || AC ,DB = 4, AD = 8, and DE = 5. Find AC.1) 9 3) 12.52) 10 4) 1539) If , , and , what is ?1) 30 2) 50 3) 80 4) 10040) Two triangles are similar. The lengths of the sides of the smaller triangle are 3, 5, and 6, and the length ofthe longest side of the larger triangle is 18. What is the perimeter of the larger triangle?1) 14 3) 242) 18 4) 4241) Which transformation produces a figure similar but not congruent to the original figure?1) 3)2) 4)42) A triangle has coordinates A(0,0), B(6,2) and C(6,0). After R180º, what are the coordinates of B' ?1) (-2,6) 2) (-6,2) 3) (-6,-2) 4) (2,-6)43) Under a dilation of scale factor 3 with the center at the origin, what is the image of point B(2,3)?1) (6,3) 2) (2,9) 3) (5,6) 4) (6,9)44) A translation maps (x, y) to (x – 5, y + 3). In which quadrant does the point (–3,–2)lie under the same translation?1) I 2) II 3) III 4) IV

45) A triangle has vertices A(3,2), B(4,1) and C(4,3). What are the coordinates of point B under the glidereflection T( 0,1) r y axis.1) (2,-4) 3) (4,2)2) (4,0) 4) (-4,2)46) Given points A (-2,6) and point B (4,5), what are the coordinates of points A” and B” under thetransformation of D2 T3,6.1) A”(6, -1) and B” (4, 5) 3) A”(-1, 6) and B” (5, 4)2) A”(0, 2) and B” (-2, 14) 4) A” (2,0) and B” (14,-2)47) Which statement is logically equivalent to “If Andrea gets a job, she buys a new car”?1) Andrea gets a job and she buys a new car.2) If Andrea does not buy a new car, she does not get a job.3) If Andrea does not get a job, she does not buy a new car.4) If Andrea buys a new car, she gets a job.48) The sentence "If __________, then 6 + 3 = 9." is TRUE. Which of the following statements could be used tofill the blank and maintain the truth value of the sentence?1) 10/5 = 22) 12/3 = 63) both choice [1] and choice [2] could be used4) neither choice [1] nor choice [2] could be used49) Given the true statements: "t is a multiple of 3" and "t is even." What could be a value of t?1) 8 3) 152) 9 4) 2450) What is the negation of the statement “I am not going to eat ice cream”?1) I like ice cream.2) I am going to eat ice cream.3) If I eat ice cream, then I like ice cream.4) If I don’t like ice cream, then I don’t eat ice cream.