Answers - Understanding Points, Lines, and Planes

.........-- 1-1 Understanding Points, Lines, and Planes • Draw and label each of the following. 1. а segment containing the points А and 8 2. а гау with endpoint М that passes through N 4. three coplanar lines intersecting in one point. Name each of the following. 5. three coplanar points 6. а line contaiГ)ed in�•neither plane 7. а segment contained in plane R 8. а line contained in both planes 1-2 Measuring and Constructing Segments Find-the length of each segment. вс 1•1 ♦ 1 1 1 1 1 ► О 5 9.АВ 10. вс 11.АС l1r::: ' �j] �'-� \ Sketch, draw, and construct а segment congruent to EF. l А ' : =IЗ 13. В is between А and С. АС = 24 and ВС = 11 . Find АВ. �--·-· ...· 26 14. У is between Х and Z. VY�t �ssWt'l, Х ?;}'_ Эх+ 2 У 15. Find х. 16. Find АМ. 17. Find ВМ. iqaj i L.·---'--••··. , _J q(ll)-��q"-LP 1-3 Measuring and Constructing Angles '1 з.1 • Чх-t, • � t ;;,7 Е 22. N 8 JЗ qx-i, =l.Qx+.:t1 qx...,.t,x+aз Вх == 8 з G 20. mLPOR = 150 ° 21. mLBRZ = 90 ° t (3xt-l-L)° + mLLMТ, = (Зх 12) 0 , and mL ТМР, = (6х - 24) 0 • Find mLLMP. мf Ьisects LLMP, '6X-t i7 • Classify each angle Ьу its measure. 19. mLXYZ = 89 ° F • 1)(; - :;i Х-= 1\ 18. Name all the ?ngles in the diagram. !:i_ffн-, .,i.. ».'F(;r,_ "�ет ! -в �t.f-.3,c �UI )-1-27 l.,(g 1 ( av -L3x-t �) J.(.p + 27. :- � .2.+ Z М is thfvrhiфoi"nt of АВ. АМ = 9х - 6, and ВМ = 6х 11ВхС. � ){ Use а protractor and а straightedge to draw • an 80 ° angle. Then Ьisect the angle. ((g'14-�'t) р Эх+1� -=vx -�ч '� = эх. -.;2t.f 1-4 Pairs of Angles Tell \vhether the angles are only adjacent, adjacent and form а linear pair, or not adjacent. .3(.g = 3'Х " .:= 1 .:2. o 26. LЗ and L 1 lf mLA ·u: ·rrc;н,«· .. ·--··"- = (7х - 12) 0 , find the measure of each of the following. 28. complement of LA 27. supplement of LA rri� -1�)�i ЯО-7х+ /SЬ-(1)(-J).) = J l:Z 1-5 Using Formulas in Geometry ГZJp__� -1xI�j . . qo-( 7 X-/;;t) = 9о- 7><+-1 :1.; /D i _ 7)( Find the perimeter and area of each figure. 29. Р= Чх+�х+f rdx-2 Р::: qx+� А- == J. ( t/x'f2,)(+К Jx + 8 2. � �J.x(�x+g) 2. А =ЧX t-l{QX ! 31. 4х 30. 12х :::L/Ex P�1t(12x) А- =- (/ л Х') .z. == I 4-Ч, Х 2.. Зх-2 Р::.qx.� � и.п:;· А = Чх 2+-1 � � (Ч, �У, t i/ = \ � 2. 3 2. i__ e_== ц1�_цл.j ..��=='Тti4X � ШJ 2х �О,З..5t\?"�144 '1. Ь = \�.3.15 Ь.:::Н. 1� f'::: �(:;l.)()t-� ('i-3) �::: L\Xt- 'l.)(-tp х- з �-,---- 2. �:: � �::: -··------· - 2.')( х - tp (х-3) )., A:::2� --tQX �!-Ltх \.U'\L : :Р: tp x-Jg М) J� .:_ -� f\-= 1f (�) 1. 33. Find the circumference and area of а circle with radius 9 in. Use the п key оп your calculator and round to the nearest tenth. :: . гL___'f\i-�. �'54 6 1- • � �-=i\ ,r 25�.6\Y\:z. · • \У) ; t-::. �1fl�) е,:.\�1{ с::б'g.5 '·:'._:, i: \У\ ' с., _ �' ' �-�� .... • •. �--·-----· =: 1-6 Midpoint and Distance in the Coordinate Plane • ___-______ J 35. S is the midpoint of RT, R has coordinates (-4, - ) and S has coordinates s ( 5 the d 3 3 c°:: E� i��)}-_� ( �:;J 36. Using the distance formula, find PQ and RS to the nearest tenth. Then determine if PQ RS. = -·· .. ·- .. . .. . ffi-::: ? � ���1��}=�;��$-�) )( = \б У . . . = \� : LЪ:11 . • •1 ) (10, 18) ::.:::г·=F.? (.Ч,1.) PQ � r<.S . . -· . .. ...... . . . . . . .. . . . х 2. 7. с-1-�&3))�+-+���э�-- r;,_-s..:�{,-з-�) +с-з-2) R6 = �(-,)�4 [-5):а. �5 =� \-\-25 :::� ?Q. � (5)�+t-l) a.. f'щ =-�2s�1 =.J2v 37. Using the Distance Formula and the Pythagorean Theorem, find the distance, to the nearest tenth, from М(4, -3) to N(-5 , 2). = '1"(�-�t-:�))�t .(�з.��У' '{Y)N = � (q"'/· + (-"5)2m N = � е, +r;z,s = '1" \(Яр �N 5�+ 92. =с.,2. ;).5 .- &1 2. :а. с, =6\Q 1 .. =с . :· �· ·: • • !· ·:· -�. . !· . е = J101q \ 1- 7 Transformations in the Coordinate Plane ldentify the transformation. Then use arrow notation to describe the transformation. 39.K'UL к J . • - • •�-й:eili·м - м L о • fre;C.O'б ➔ f\ ,е,1е, 'D '6' : -�{1 (5)'\ • • : :.... -�'t.�--������� �---· ·---� :·,.,!;( ;., ,!, .,-· .J(-sJ ч-') � (.-2, u) 40. Find the coordinates for the image of figure JKLM after the translation (х, у) ➔ (х - 1, у+ 2). Graph the image. ·с .... L(\ } -\.) :г : : м (--2.J -.2.) х ' (, ·-·-�------· - --------------- ·--·-'' 41. А figure has vertices at А(2, 4), 8(-5, 1) and С(О, -3). After а transformation, the image of the figure has vertices at A'(S, 6), 8'(-2, 3), and С'(З, -1). Graph the preimage and image. Then, identify the transformation. \