[>, 30 8 ~J - J 2 1 \ g - ~ lp) l.J.s -4 ~P , 3 I lc tt iL - }lo > 3 1~ 3 3/~I

6-2 Notes: Properties of Parallelograms

Any four-sided polygon is called a quadrilateral. A segment joining any filo noncol1S'"ecUfivevertices is called a diagonal. A special kind of quadrilateral in which bofh pairs of oppositesides are parallel is called a parallelogram (this is the definition of a parallelogram).

You can use what you know about parallel lines and transversals to prove some theoremsabout parallelograms.

Def. Parallelogram ~ Opposite sides are parallel /.:. Parallelogram -+ Opposite sides are == ..,.:. Parallelogram -+ Opposite angles are ==.:. Parallelogram -+ Diagonals bisect each o,her.:. Parallelogram -+ Consecutive angles are supplementary ~

If each quadrilateral is a parallelogram, find the values of x, y, and z.105° 31°

1. 2. 3. f;: Z~ -::..~q

o

~~ 13 ~::z =- rO~ ,

4. In parallelogram ABCD,mLA = 3xand 5. In parallelogram RSTV, diagonals RT andmLB = ~x + 4Q. Find the measure of angles VS intersect at Q. If RQ = 5x + 1 and

-A,:-S',:-C,'alld D. QT:3x + 15,find Q--r-. - ...,' 'RG:.. 5;{\ + \

O~~~~+-tt 1--+ \.{-o:: \ go' 5' 5x -+- I -=- 31' + (5 R \"'=. 31'>-\-\5

." I}-=-{L[--V, X =: ~'O ~ 'X -=-., \ ~

T 'X-=-i.\) G f'f\ L f\ ~ MLc.;~_{PO ~

\l\L~ ~ \')j LD ::-\~G GT =- 3lo ~Explain why it is impossible for each figure to be a parallelogram.

10

%--=- 7.3

~~ (3

~ :: {:o1

6. 7.

8. AB = 3x + 2y; Be = 3; CD = 7; DA = 2x + Y

Find x and y so that ABeD is a pcrnllelcgram.

R ry: +- ~ ~ 3 ~ ~~~-.d- 't-

311C -\-- ~ -=- 1 % =- -I .

(" ll-:.. 53'j{+:;" ?:>-d-.?\)=-7 0

~'): + (p ~ Lf- rx- ~ I ~. B

-~=-\ "K\S~9. mLA = 2x + 8y; mLC = 4x + 3y + 54; mLD = x + 2y + 16 ~'1V

d 't -t_?_~ ~ 4-'" +- 3?!--tSY- ~ ~ + g- ~o-- + r ~:::- rg {) y~ cr\\#

6i + 5 't ~ ~-:tIO; CO- I t" ttJ Dr:-:-:\-)( -l')G ~ =- .s4) \~

'tJ.-101":.-'OI .~)+I01~ .,,"

1~ :. 5'-

1 c

3(V) .•.10' ':..Ie.'fIll:' ,,,,0~ ,..• \

10. Find x so that ABeD is a parallelogram: AB = x2~3; CD = 2x+12"1,'1'- 3 -:..d..'f-+- \ 7-'1- -5::'0 ~+-3 :::0

"f.'2-J-r. ~\5 =-0 (X-=-s X-=--2>]

('1---5')( 1-~~-=-O

11. PQRT has vertices P(-4, 7), Q(3, 0), R(2, -5), and T(-5, 2). Determine if PQRT is aparallelogram. '1 - 0 ~ .

~0'1,1) G, b,\)J ~ PG "0- -'I -~ ~ -1 = -I 1\--- ~1-5 '7 ./\P~-TR.:;· ::. ~ -::. -I

~VV -5-2

.LJf~ PI ::. ']- do- -=- ~ ~ 5\ (-5 1'21 . -Lt +-5 I 1(

D

------------ ---

GeometryWorksheet Parallelograms

~me~ _

Date. -JPeriod,-----

(1-8) Given po.ro.ttelo9f'amTAXI, solve for y or z or both. Also,stote what property of the paraltelogramlhol ou Qr~ US) (exam \e~ 0 osite sides are c ruent)

4.mLXTI=4y-5;mLTXA=3y+l0 '+'(t-5:: 3(tT \0

'&-~\S

'(t=-IS \\ ~~~ aJl:t.~L6. T~:-:--t---=;~--~~X

1 AX;; 3y' TI :; 2y + 10 - .;,g u. ~... ~'~'-.'Q ,- . , .

d.~-t-IO!:3lJ

to ~ 1r

2. m LTAX = 2y - 5; m L TIX = 3y - 20,y

1¥c s =,_'J.\1-5 = 3,!--2 0

15 =-~

3. AM:; z.x2 + 2x - ~;

'X-~ to1M :; x2 + lOx'" 5

2. "2-!l~ + 2''(-15 = 'I..+ \0)( +5

}.~ - Soy. - '2.0 -::..0

C« +2.")( X-IO) ::'()

'X = -e- 2. {i-= \0 \

T~------~~------~X

T~--------~~--------~X

5. TM:; 3z; TX:; 3z .•.18 t..'t= 3'2:-+-\83z-=\8

c;:;.(,.

~.~ ~ ~ T~~~-=:.;£--=--~X

6. MI:; 6y - 5; AI ': 2y + 15 \"2. (J- - \0 ::: d.'(t+ t 610'(\::. as

T~-------r~~--------~X

, r: --'",·~~5-t)

" / t'\19'~r-5:':·t-~-dZ ~ ~)(

fly. "&

7. AT;;; 7y + z: XI =: y of- 28; TI = Y + z: AX = 5

1f.~rJ.

&.~~.T::\~ -r~=-Z~. - .

't,+ t--:. ~.' .

8. m L TIX = 2z + y; m L TAX = z + 20; m L ATI = z - y -~"Ff L5 s:

~.L.s ~.'«t :: - 4 ()

r z: lDO~'2--Ht::::. 2-+20

2-+'(t=-'-.O

-2:-'6+C Wc::iS'v

2~ -~::.. \G 0

.J. "2; ¥- '3- :: l:- + 2 0-

~-i-~.;: 2-0, .

clC- =- 'ioU

In problems 9-12, find x and y so the KMNO is a parallelogram.

9. KM = x + v: MN;;; 2y + 6; ON = 2x - y; KO =: 3y

X=-\2.

10. KM;;; x + v: ON = 3x - 4y; m L MKN = x + 5; m L KNO ;;;2x - 10'''1( +5 :::a'f.. - \ 0 )( 4- 1t:' 31-~ 4 i-

X c I ~ \ 5 =- x 5,!- -:. 2 )( :::0 2>0

lJ-.:. b 'tt -::::.~

11. m L KOM = 6y + 1; m L KMO = 3x + 2; m L MON = 2x + 8; m L OMN = 4y + 7

G,1t-t\ = 'f~-tl 'b~-t'2. =-'2.~T"g

d.1::'\:>

't -=-3

12. KP= 2x + 4; MP = 6 + 3y; NP = 15 - y; OP = x + 4

)(=5

'Y-- 'be \\-d,~)::'d- 'lx '~ ~s'Y -?» +-\o~ :: d.., x -=- t>

'1 'Y-::: 2>5"X--=-5

~----."M

o

\O+~= il

~=\

6-3 Notes: Proving that a Quadrilateral is a Parallelogram

You can show that a quadrilateral is a parallelogram if you can show that one of the following is true.

Def: Both pairs opp. Sides /I -H- Parallelogram

.:. Both pairs of opp. Sides == -'-J. Parallelogram

.:. Diagonals bisect each other ~ Parallelogram

.:. Both pairs opp. Angles == -+ Parallelogram

.:. One pair of opp. .Sides ere both II and == ~ Parallelogram

Determine if each quadrilateral is a parallelogram. Justify your answer.

Determine whether quadrilateral ABeD with the given vertices is a parallelogram.4. A(2,5), B(5,9),1(3,-1),.2f(6,3), --: . 4/ 1

o ~ c ~ Iff!> ~ /3

\

.- ,,+-\. \\~ eD =- ~ = ~

e.., -6~ -=- -to ~ \\4D:: - Co )

1.

D

5. A(-l,6), B(2,-3), C(5,O), D(2,9)~

2.

~\~~

(pcWv ~~~. (j

3. ~\~---~ --.? .

/Y1AJ"" -:;;tk i\.~ ~~ ~. /.J~ OA/:tiVl

~~

Explain.

.~ 46-::

-r=:~

~Ab

- -'2>-00(J:: 2-5

C, -1.0--d.+ \

GeometryWorksheet - 6.3 Parallelograms

Name _

Date Period----------------~ -------Are the following parallelograms? lfyes, why? (use one of the five reasons from section 6.3) If no,tell what else would be needed.

4. /11& - i'rffY L 5 4~

"'~....;6;.;;.o._1_20_. _...;.;llJ~7

11. 1f4< t:ft' 4ddM=

9

\ \9

14. ·r-L?f44M il13'rw LS~

7

U7

17

C?l17

12.. ~

M is the midpoint of AC and lID

L><7BD C

.r:«lZ:J19

State whether the given information is sufficient to support the statement, "Quadrilateral ABCD is aparallelogram." If the information is sufficient, state the reason.

18. ABIICD and BC IIAD W~VJ) 1/ fr.--, __ -:?I

19. AC..LBD and~=OC /Yl4 a: a uL::.-----/C0\\cl) ~,

~r\ _ _ , '. Iv' uilJ20. Ll:; L4 and AB:; DC ()rY\,R- (fCUJl." '-w .acau > Q...'1 .

~ 21. Ll:;L4 and~g) AD 1\ bG ~AUdt£),; 1\,,,0

22. AB == C~ and BC :: AD ~~ (JtHi-zl 1ftf ~-=-

1f> ~vU\\

24. AB:; CD and BC IIAD .~ ~Y fYYt1l- (}CJ-iu /.ucw J-;; ; ~/1'.--t

16. AB::CD and ABIICD

17. AO=OCandBO=OD

23. Ll:; L4and L2:; L3

25. BC:;AD and BCIIAD

26. L2:;L3 and AB IICD

27. L2:; L3 and BC :; AD

D

'C

28. L2::L3 and AB::CD .~ cJ

29. LBAtJ= LBCD and ~BC == LAL?C"\)

30. LBA{}) is supplementary to LA,DCLADC is supplementary to LBCD

6-4 Study Guide - Special Parallelograms: Rectangles, Squares and Rhombi

A rectangle is a quadrilateral with four right angles. It follows that since both pairs of opposite anglesare congruent: a rectangle is a special type of parallelogram. Thus, a rectangle has all the properties of aparallelogram. However, a rectangle has an additional property:

.:. Rectangle -+ diagonals are congruent

A rhombus is a quadrilateral with four congruent sides. Since opposite sides of a rhombus are congruent,a rhombus is a parallelogram and has all the properties of a parallelogram. The diagonals of a rhombushave two special relationships .

•:. Rhombus --> diagonals are perpendicular.:. Rhombus --> each diagonal bisects two angles of the rhombus

Is the parallelogram a rhombus or a rectangle? You must first determine that the quadrilateral is aparallelogram and then you can use one of the following theorems to determine if iT is also a rhombus or arectangle.

V.:. Consecutive sides of a parallelogram are congruent --> rhombus.:. One diagonal of a parallelogram bisects two angles -+ rhombus.:. Diagonals of a parallelogram are perpendicular -+ rhombus.:. Diagonals of a parallelogram are congruent -+ rectangle

v' .:. Adjacent sides of parallelogram are perpendicular -+ rectangle

A square is a quadrilateral with four right angles (a rectangle) and four congruent sides (a rhombus).Therefore, it has all the properties of a parallelogram, a rectangle, and a rhombus. Also, to show that aquadrilateral is a square, you need to show that it is a parallelogram, a rhombus, and a rectangle.

Example: ABCD is a rhombus. If mLADB = 27, find mLADC. 54- ~

Since each diagonal of a rhombus bisects a pair of oppositeangles, mLADC = 2(LADB). So mLADC = 2(27) or 54. r:A B

Use rhombus PQRS and the given information to find each value.

1. If SQ = 24, RP = 10, find SR. i?>2. If mLPRS = 17, find mLQRS. 34-°

3. Find mLSTR. q 0

5.....- _

4. If SP = 4x - 3 and PQ = 18 + x, find the value of x.

i'l--?>:::. \:st'i- X.=-13 '1--7- J..\

Use rectangle RECT and the given information to find each value.

5. mLRCT = 30°, find mLETC. 36')

6. If RC = 5x + 2 and AE = x + 14, find the value of x.

Determine whether EFGH is a para.llelogram, a rectangle, a rhombus, or a square for each set of vertices. :iState yes or no for each and explam why or why not. Show work to support the exp.lanations. 1/'-'78. M(l, 5), N(6, 5),0(6,10), P(l, 10) 9. W(5,4), X(3, -6), Y(O, -10),Z(2, 0) .L-J-J !

rv;~ N s\ope('f)N =- -.~~: ~ 0 .~. s\~p~ 0)X = ~-'r_~~~::c5l '{i _ _ I( Slop" 7'-(_ -,o-~ -10 \I

I \ o {O (0 0 I:::-- z= - = - -5S Dpe. \ o ~.- ~ ' . 0 - 2 -2 -I to ~~ >1 > no-\-J..t slof€ fY)P ~ ~ ~).,V(\~ (. \( ~ lope LA.) "2::::=: ~_~ :0 ~( \ \

r 0 ,-" _ ~o _ ))/yld.U~ s\ore v: '( --;. - to -t-IO .= ~ jSlor v N 0 - G - b - D ?:> --c) 2>

~ lODe IV\0 = ":.::..'.-0 ~ -:2. ~ \ } 51Dpi. W'( = ,:!:-r \ 0. = Ii \u \-10 -s ~1- 5-0 Vlo+..l

- 5 = r o -5" __ J \ ~:::- -~ -10Slope \-\?::. ~ :> -S - \ s ope. 'f.. '3-2 z:

, .j \ \parallelogram: ~c S - °rf SIt.-' e.srectangle: ~es - C.OI{IS. s;c\es 1-

rhombus: 't€ "> - d. \ Q%, l

square: ~e s - bo'Y\~reC-\-CLh3\e # rho\lY1605

parallelogram: '7f s ~ 0 f f side s \I

rectangle: '(10 - c 0\/\:5. 5\ de S no+- i

rhombus: '(10 - d\o..~. hO-\- ..L

square: VlO - VlO+ rec\-c."'Jk:. o...vd ,hom6us

----------------------------------------------------------------------------------------------------------------F:----- r::D 10.~(1,10),E(-4,0), F(~,~:~~(1~ 1i2~::: 11.R(5,6), E(7,5), 5(9, 9), T(7, 10) _I Is/ 7 5l6pe DE - \+~ - 5" 2.l . ~ (0-5 \ I

I r 1\ S\ODe R6 7- -. ::- - ~'--c;;. \ -.- _ ;1-\ 2 + I 0 _ '1 \.s -, - 2... . \j) \ S Dpe G F- - - "'- --::: - cI.. - \

,-12- -~ ""- V\o\l 5\0 e T~::. \O-q - _\/ .,. f '-'1 - -2. ~ \

\-- \0 - \ 2- - 2. __ 2. I -

sore DG -=- ~ z: -1\ \r } S\Dpe R\" z: le.:IO;:; -~ -=- ::L3" II _ 5 -, +z, \I

\ - 0-2 -2-. oJ- \S Dr-e EF- c, - ::=- \\ ::: \I :; o(.?t. £5 = ~:. -::.1.. .z: 2...

-4-1 - I ,-"I - 2-

slope '0f-::::. \0-2...;::..1. z: -~ 5\60 B to-q - -.l ",-?" ~\-1 -(0 31 \ ~e. "-::. S -0..- -t\ 4- Yio-\--j_

. -~ 0-12. -\2. ~ - 5 10 ...I rS\oDe t:..G z: __ =: ~ .: - S\OI?e. \E.. =- ~ z: unoe +.I -4-12... -Ito If I ,-I

parallelogram: '6(: sop r ':,\cte. s \ \ .

rectangle: VlD! COVY:; Slc\es nc-\-lrhombus: ~e s d i6..6 ,..L.

square: 'f\O \ V\o-i-'eC.+a..Vid\e..

parallelogram: dc:S - 0 f r 5 '\ de,S \ Irectangle: 'tie -s co,-" '), s\c\es lrhombus: (\0, d\()_'<~' \\o\-lsquare: '00 - V\ 0-\ f "'oVV\ Ie tJ S

Geometry WorksheetRectangles. 5quares & Rhombi (6.4)

Name. _

Date__ _Period, _

1. In rectangle ABeD, AB= 2x + 3y, Be = 5x - 2y, CD= 22, and AD= 17. Find x and y ..) (.9.'~+.3 ~.::.J~) i.t.~ +1., ~:. 4~", \'(,~ s:" \ Aro::::::---,c;,...t::,~-8---:::=o'1B

-3 ( 5 x.- a- ~ = \ 'I ) 15"l. . 10% - 5 \ . _ d \1 5't-J 'if, u· \ q ox, = q 5, .~ - .., ,

In the diagram for problems 2-7,QRST is a rectangle and QZRC is a parallelogram.

z2. If QC = 2x + 1and TC = 3x - 1,

find x. (;>

a x .+-\ = :3~ - \ Q tE-------"'" R tn L G 1 R ~ \ '-\-0 ,{ J. ::. )<. \

T ~--------~s

3. If mLTQC = 70, find mLQZR.

4. If mLRCS = 35, find mLRTS. z 5. If mLQ~T = mL_TRS,find mLTCQ. Z

Q ~----------=::..

T 56. If RT = X2 and QC = 4x - 6, what is the value ofx?

').

y.. z: S?x - \2-'2.

'" - 8)<'H"2 ::.0 Q ~----------,;;;;.. R

l~-2.') l", - ~) =- 0\ '" ::. do )I; Z ~ \ T ~ ~::::..J 5

z

Use rectangle STUV for questions 8-11.c

8. If mLI = 30, mL2 = '75o

9. If mL6 = 57, mL4 = 3.3 .10. If mL8 = 133, mL2 = lD 1.0 tJ 5 .

'1 u 011. If mL5 = 16, mL3 = _.....:.....'....!.-

7. RZ = 6x, ZQ = 3x + 2y, and CS = 14 - x.values of x and y. Is QZRC a "special" _parallelogram? If so, what kind?'i\-\ ':> a.. t'hom bu..$10')( ::. i4 -)( z

. ~ ~,-, ~ -=- \ '+ .,- .3~~\ )( -=;;t\ \ ~:: -"3 \ Q:',~~~~~

~'1a'r\::'\2. do ~(p

---------------------~~

12. ABCDis a rhombus. If the perimeter ofABCD= 68 and BD= 16, find AC. B', \.

~::\I \ AC=-.$o \

A7. '1. 2-

&""'A =-\1'2-'f.. -;.. ~as

X-=- \5

13. ABCDis a square. If mLDBC = X2 - 4x, find x.

)(:-4"~ 4S A0.BX - Y )(.- 4-5 =-0

(,~.,'-q)()(.+5)=-0 D '6 e

\" )('::q X ::. -~\

c

"

Use rhombus ABeD for problems 14-19

14. If mLBAF:: 28, mLACD:: d-.8 '.,15. If mLAFB = 16x + 6, x :: 5..d.5. 1(0 X -\--\0 ::: qo

16. If mLACD = 34, mLABC= \, J- , .17. If mLBfC :: 120 - 4x, x:: 1..5 "

\:2...0-' 1.\ 'f..:= qD '?,o :.l\ ~

18. If mLBAC:: 4x + 6 and mLACD:: 12x -18, x:: 34 ~+(.,.~ \2 y.. -\ g

a~~8~ \19. If mLDCB:: Xl - 6 and mLDAC:: 5~,+9, x:: ~

J.(LbA-c..')= L'DC.£> ~2-to~-;l"l::0~ .. '

\bx-+\~ ::.. ~2.-Cc ().-\2.)(y..4-2)=-O20. ABeD is a square. A8:: 5x + 2y, 21. A contractor is measuring for the foundation of a building thatAD :: 3x ~d Be :: 11. Find x and is to be 85 ft by 40 ft. Stakes and string are placed as shown.y. , ~('Y'1-- J \. 08 The oetside corners of the bund;ng will be at the points where the£ i : ',:, ' strings cross. He then measures and finds WY :: 93 ft and XZ :: 945.,. -i-l 'a ~ \, 3"- 't u ft. Is WXYZ a rectangle? If not, which way should stekes E and.f

(~ '. _, \') be moved to made WXYZ 'a rectangle? ':).. ~v "'J.-,'3- -

t,,~ - 1't :::.1..2- D \' C not ,ecl-~~~\e 6ec.a.use 1-1---85ft----Idlo..3oVl<l.\.s a:ce t\o+ ~ '_, F

G'~' :;::::-:------~- D T

HI-;~~-----~--~..~~_c401..'--,

\\'X -:. 33

r 'X. ~ 3-l-,5~a~ -=- \\

'"~-a~\-~=-it

A B23. ABeD is Q rectangle. Find each diagonal if

3cA~,=9 and BD:: 4- c, 0c": Q~- q c..oc, ~ '+_ c, \....2_C. :;:-=-O.:.::;(.,;.-._-~1'1. C.=-3

22. A8CD is a rectangle. Find the length of eachdiagonal if AC:: Z(x - ,3) and BD= X" 5. bB'

~~ -\0 =- ). +-.5 t) ,C

\')(- \\J (1C:; Bt> = -I'~;;j,:Given rectangle QRST" 0\ J.C 24 .' If RX == QT , find mLTXS.

10 e 5 2~. If mLRQS = 30° and QS :: 13, find SR.

(0-;).. 2~. If mLQST e 45° and QT = 6.2, find QR.2.7. Given rhombus ASCD.AB:: 5x .•y - 1. 8C :: 18, 28. Given square PQRS, SR = X2 - 2x. QR = 4x - 5.CD:: 8x - 2y + 2. ,Find x and y. Find x, SR, and QR., ..•

~

%-+ -I:::I~. 5't-+-""'k.-8~11 2. , -s p o~_ ' . q'J!--:.~'7 B C ~ -or~::.4"'- '

, ~i-,- I ',' "Z., "'~~.3l /: '1- -bx+-5'~OgX-;}'t+-2""'~' ( ~4J ~ i:«> 5)(~-\)';'O

~ . '3 . <? \.')(.c:.S\;>4tI--x. -,a- -.:.'~: ~ R ~ Q ~ -=- \5"

Determine whether WXYZ is a parallelogram, a rectangle, a rhombus, or a square for each set of vertices.State yes or no for each and explain why or why not. Show work to support the explanations. For 1-;'fexample, if you say the sides are parallel then you need to calculate the slopes. / _ l,29. W(5, 6), X(7, 5), Y(9,9), Z(7, 10) Slope \\Ii::.. ~ =....L 5 . z. y

I \ 5 -, - 2. \\ .-- Ic-q 3

Parallelogram: cpr ,:>\Ae-; \\ s\cre.. -n -;.'3~~~:; -~ __ \ s\ope W'(-=- 5.q"~-~ . - 5-10 . f

Rectangle: W \"1 5,· Sic\es l s\O?e.. We ~ ~ z ~"" 2:1 6\o~ey.=t :;..;::J::u.rcle5-, Z. ,I

Rhombus: i'\o- c\t{(..%- hO-\-.L store N: 5-« _ ~ _ ' I~- 7-2-

Square: no - v\o~ rho\'Y\ bOS

30. W(-3, -3), X(I, -6), Y(5, -3), Z(1, 0)

Parallelogram: ~es - 0 ~ p Slc\e~ \\

Rectangle: l')O - to'ClS ~ \ d es no+...L

Rhombus: ~es - c\w_% .. L

Square: VlO'- n,o+ r e c\- a.V\S \e

Determine whether EFGH is a para.llelogram, a rectangle, a rhombus, or a square for each set of veEtices. FState yes or no for each and explcin why or why not. Show work to support the explanations. Foro,example, if you say the sides are parallel then you need to calculate the slopes. '.

- -3-D G31. E(O, -3), F(-3, 0), G(O,3), H(3, 0) S\o~e E-F 0:: Oi-~ -= -\ ~ \\ \-\

Parallelogram:~es-off's;c\e6\l s\orei~6 z: ;~~ =-~=-\ )".l. s\ofe·E:6-=.-~~=\'H"de.\

Rectangle: \tes- C.CI."S, Slde51. S\opeE" ~ - ~-6 =- ::.1=. \ 1/ 'F~ - 0,-60-3 -0 Slope - .:::;::; ::: 0

\ 1Rhombus: u.es- d,o..Q. ..L SIc 0e 1=-6:: 0- ~ _- 3 _o 0 \ - -:::-:;'_\,- ~-o .J

Square: ~es- bo-\-\-. rec\..~ rhoMbv.s

32. E(2, 1), F(3, 4), G(7, 2), H(6, -1)

Parallelogram: ~es'-0f'f S\des \\

Rectangle: Y\O - Con~', SI'c.\es ¥lOt-.l

Rhombus: no·- dfo...fr i'\o-t- .J.

square: no ~ neA re.c\-o. \"\~\e:.0'- '('hom buS