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Unformatted text preview: For the following problems, the points A = (37 2), B : (47 7), C’ : (—27 5), D = (O, —3). 1. The vector A33 2 b <\ ) 75>
(a) <1g5>
(b) <7,9>
(c) <—1,—5>
(d) <12,14> ‘\
2‘ The length of BE: (/(91 ’13 (a) x/éngm MK’.
(10} M—x/E 0) \f8—
m —+ A i 1"
3.1fAE~< 1,2>, thenE~ (Ll, (4,4) (0) (3, 4)
(6 4 (d) , )
4. Are vectors Ab and 0—D orthogonal? < * (2,“)
Tie; 5t “V
(a) yes “d/ﬂl  *
‘ v 1/ w 4;» ~
00/ 0 rr” A " 3 5. Find the area of triangle ABC: N; I, ‘ {1.
HQ, “*2 J x r
(a) WW3? Ki 0‘5} 33> ‘
(b) 28 Mm 4,, ﬂ: (C) 7L J. I
w»
6. <2,9><—4,l>: (§L< —6, —8 >
(b) 1} , A O
:3 " f‘ L'Ur’Tr’i’r’L,  ’ ’ Q J»? »~ I ‘j
 , [J , ‘ /X '2, ,3
_. 13 , gr
' a.) 743 (c) <—8,9>
(d) 38
7. Find<3,1,1> >< <2,2,3>:
(a) <:1 7,4 > ”153 l 1Z, 33
(b) <6,2,3> "Vb—Mm“
é£:)< L—7,4:> ‘ l w3'ZLIl
(d) Si Medan" 8. True or false: Every 3zonogon can tile the plane. ue g (b) False E 9. A 3zonogon divides into how many parallelograms? ea n7”? V": 6 (a) 2 9
a 2
(C) 5 ((1) none of the above 10. Which regular polyhedron has exactly 6 vertices?
(a) tetrahedron
b cube I’ll/{HM
@octahedron
(d) dodecahedron 1 We J};
(e) icosahedron — ’Kf) SENS 11. If the regular tetrahedron is truncated at the l/3—points of each edge, how many faces
does the resulting polyhedron have? (a) 4 (d) 12 12. A semiregular polyhedron has the Schlaﬂi symbol 3.5.3.5. What is the spherical
deviation of one vertex? (OOH of Mr! 0% [,3 :5 3 (17» bus/5 3a~waa (
13. A polyhedron with 10 faces and 36 edges has how many vertices? (a) 24 t: A] «Er/«,7. b 26 LO + \l ‘~ j;
z. I; c 8 "’ (d) 44 14. A semiregular polyhedron has 14 faces and the Schlaﬂi symbol 3.4.3.4. Find a module?
for this polyhedron: , L> (£31610va if) 1" {l (0%
7a Li L? (a) 1 triangle and 1 square Z; a :3 ,. .3 j: .., b 2 trian les and 2 s uares , ( ) s q 215 T ﬁg (c) 3 triangles and 4 squares 3 @ 4 triangles and 3 squares Ll A “l” (e) 7 triangles and 7 squares l 15, The Schlaﬂi symbol 3.4.4 fails to be a polyhedron for which of the following i‘easonsﬁ/fwtétélj‘fl (EM
(a) The spherical deviation at a vertex is not a positive number. l) (b) The spherical deviation is positive, but there are not a whole number of vertices.
(c) There is a whole number of vertices but not a whole number of edges. (d) There is a whole number of vertices and edges, but the number of faces is negative. The vertices, edges, and faces are whole numbers, but no module will work. will";
16. trahedron has an edge length of t and a volume of 5. What is the volume of the
octahedron whose edge length is t? __, , 7
, V56, {3 6 5:
,/ ,r i X i Eh I @0 ml}, ,4 .. i j . v. (,7 2/0
(c) 20t
(d) 202:3 (e) 125
17. An octahedron has a volume of gg. How long is an edge of this octahedron? A mﬁmk (3‘3)
0 8 r (<93 3
(6)3??? \QLTL "3 «elm ,Ffr_ee..Respon§e,=, The diagram above shows an icosahedron inscribed in a cube. The edges of the icosahedron
have length 1. Points A, B, and C are vertices of the icosahedron. Points D and E are
the midpoints of the front and top faces of the cube. Point F is the midpoint of the edge
shared by the front and top faces of the cube. Complete the following steps to ﬁnd the
length of the edges of the cube. ' 1. AC : __l__ (Find the numerical value of this length.)
x
2. AD : "/3: (Find the numerical value of this length.) 437
3. CD : "£7." (Find the numerical value of this length.) (Hint: Pythagorean Theorem.)
4. BF : a: (you don’t yet have enough information to ﬁnd this value, so we’ll call it 3:.
U . 7,
5. CE : __:‘_2: (Find the numerical value of this length.) V “l3 "1 f E :5 v “N if 6. CF 2%}; (Find this value in terms of n.3,» )( 3"" 35%“ ,2 “L 4'»
VJ ’L ._ 2.: a 7}. ,é.
7. Use the fact that CFD is a right triangle to solve for x. x = ___ _. 3L 4 I ’ " L; '1' 4v)
.1’ / ti 1,
8. How long is an edge of the cube? ls l‘ W 7‘ "Zr “ O ....;,.... r '? "2 . I _ ¢ 1/)“: k 7 “3" w l 'L 0 <3 ( ...
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 Spring '14
 DragaVidakovic
 Geometry

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