Similarity Definition (G.SRT.2 Wkst 2) Guide
What is a transformation?
gy,e' "{" trtAl'
t/\'\416'1;Ab
0
tl Vc'*;"s)
+w-+ i^,.'lL q g'*'liee2, evtl wif,r-
What are the isometric transformations?
lonoga \ t
{, Pre-)vlna-Xz G-*
Cst'*'tv'Pxt
e.lBlr.:.
q Izo+-irge'd-{t*+
;i'fi5
What is the definition of similarity?
k
what
is a
:,vn7\ '-i\
4,n1V o'fu7w^u- , {
c-vlotL-u+z
simitarityr,{l}ffir,
*t
"
Aagaa- IB € tr
AABC
-
-
*>oxy6"'*'J'-*S +l\rt
C*
As=w
-to
DT
€F
LAE LD
/B
/.<
U LE
y
i'i'\a-P elrz'
LF
AMRG
lM=
ASTV
* sn!-)
G+*.o t F,-+lu) / Trans u'.w)
What are the similarity transformations?
5a"^^''
srLe
Lfr
RG GM
BC cA
A'I/QY
ZT=
O
Determine two similartiy transformations that
would map LOBA onto AORG.
Cn,
followed by
t
(A oBA\
49 :MR
AC
MG
y5
sr
WQ
TV
qy-
4{= w
TV
QY
Determine two similartiy transformations that
would map Quad ETHP onto Quad ODBA.
-{/'
azs,n-
l}*.t frw t
G.SRT.2 WORKSHEET #2
NAME: _______________________________
1
1. Name the similarity transformations - What makes them different from the isometric transformations?
2. Why are isometric transformation a part of the similarity transformations?
3. Determine whether the following are (T)rue or (F)alse.
a) Similarity transformations are all isometric transformations.
b) Rotation is a similarity transformation.
c) All transformations are isometric.
d) Dilation is a non-isometric transformation.
e) Stretch is not a similarity transformation.
T
T
T
T
T
or
or
or
or
or
=
AG
DH
F
F
F
F
F
4. Given that ∆AFG ∼ ∆DRH. Complete the following.
∠H ≅ ∠ ______
DR DH
=
AF
______
∠D ≅ ∠ ______
RH
______
5. Pentagon ABCDE is similar to Pentagon RYMNT. Complete the following.
∠C ≅ ∠ ______
AB ED
=
RY
______
MN CD
=
RT
______
A
C
M
N
B
Y
R
E
∠T ≅ ∠ ______
NT RT
______
=
DE
AB RY
=
BC
______
D
6. ∆ABC is similar to another triangle. Provided is some information about the two triangles,
BC AB
. From
=
DR TD
this information determine the triangle similarity statement.
∆ABC ∼ ∆_________
7. The two figures in each question are similar. Create the similarity statement from the diagram.
a) Pentagon GYKMR ∼ ____________
b)
∆JMT ∼ __________
c)
T
∆BAC ∼ __________
G.SRT.2 WORKSHEET #2
Y
G
M
A
R
M
2
A
E
T
C
K
J
O
B
B
B
C
D
A
J
C
H
T
8. Determine the sequence of similarity transformations that map one figure onto the other thus establishing that the
two figures are similar.
a) Determine two similarity transformations that would
map Quad. OBCD onto Quad. OHTE.
b) Determine two similarity transformations that would
map ∆OBC onto ∆ΟGT.
____________________ followed by _________________
____________________ followed by _________________
c) Determine two similarity transformations that would
map Quad. GHIJ onto Quad. RKYT.
d) Determine two similarity transformations that would
map ∆MNT onto ∆RFH.
____________________ followed by _________________
____________________ followed by _________________
G.SRT.2 WORKSHEET #2
3
9. Jose claims that he was able to do 4 different double similarity transformations to map ∆CDE onto ∆MPN. Let us see
if you can do 4 as well. (Show the steps)
a) Method #1
b) Method #2
____________________ followed by _________________
____________________ followed by _________________
c) Method #3
d) Method #4
____________________ followed by _________________
____________________ followed by _________________
G.SRT.2 WORKSHEET #2
4
/.r*r.,
woRKsHEEr #2
1. Name the similarity transformations - What makes them different from the isometric transformations?
Po"[a"k^* ]
(tLl4eil+-*- t
{va^9t a-(i*- \
D)
[c"fivt-
1 ; $,,^.-c
*
y;*o?[uk
"r,
z
2. Why are isometric transformation a part of the similarity transformations?
3. Determine whether the following are (Tlrue or (F)alse.
a) Similarity transformations are all isometric transformations.
b) Rotation is a similarity transformation.
T
T
T
T
c) All transformations are isometric.
d) Dilation is a nor]i-isometric transformation.
e) Stretch is not a similarity transformation.
4. Given that AAFG
- ADRH. Complete
DR
lH=l
AF
-=
@
or
or
or
or
or
@
F
@
F
F
the following.
DH
E
,ftG
tD=t
E
A
RH
AG
DH
5. Pentagon ABCDE is similar to Pentagon RYMNT. Complete the following.
ffil
lC=l
MN
RT
CD
E
#=fi
-=
6
lT=l
5. AABC is similar to another
triangle. Provided
is some
Yr'^
HP.
D
information about the two triangles,
BC AB
_=_.
DR
TD
this information determine the triangle similarity statement.
AABC
-A
7. The two figures in each question are similar. Create the similarity statement from the diagram.
a)
Pentason
GYKMR
-
1ert
ftEDcb
W-C
M
^J/1
uu,
b
c)
ABAc
-
ATtl
{
l-rom
G.SRT,IWORKSHEET #2
sequence of similarity transformations that map one figure onto the other thus establishing that the
two figures are similar.
g. Determine the
a) Determine two similarity transformations that would
map Quad. OBCD onto Quad. OHTE.
b) Determine two similarity transformations that would
map AOBC onto AOGT.
D, ,r.
followed by
( Aw.)
(aon'c,
foltowed by
#
#
{ta*"
.B
i :4
i
Y***
Ar4f
'
:n
i*
.;.. ,-:.,..,,.
, '#
:d
I
,kr .*i: ",ti 'r.:
..* -e
.'Bl
o
cf
.-.$
r€
.i.,...,,,1
,.4
C;
;*
-B
*6
,"-1-,- : ' ' '
...-.t .,"......r...........-,* . 1..--:
c) Determine two similarity transformations that would
map Quad. GHll onto Quad. RKYT-
1I
l:
ii
al
ij
t-
d) Determine two similarity transformations that would
map AMNT onto ARFH.
(Nq'
ov T <'*>
@tottowed
followed by
,'.
A
- *-s
H
i':i
l, i.,.;..
v\
l:
ai-:i
';... 3,.
, ,S
);
: '''l *
1 :i.f
i
''a
, ..-fuf. .;-
.....:r ..,.;........).,,
.
;
r-
.;:'I
"',:",
i
,, i:l
"'-H
I : i r,.
$
,
l
';=O'i
8
'&i &.':
&:
:,.i',--;: -, !
*
.
'r.IU
-'- 1
-11
s:: *j,t
SrI &",:
:r;l)
. ...i..
r::jll:
+.
-- "i"T--'+
tt
;..;
&'.
*
tvl
.....,
i
"
,/":\.
., '\
&
..:.*
:
.-s-. ,-!'-'
:4:
,/4,.
-,... ,i't-'
-J:.'
*'r)
l(
mu",lher-
i c*n'+
On
ts
G,SRT.2 WORKSHEET
#2
3
9. Jose claims that he was able to do 4 different double similarity transformations
if you can do 4 as well. (Show the steps)
v
(aon)
unq
ACDE onto
AMPN. Let us see
b) Method #2
a) Method #1
A
to map
4l o, v)
followed by
followed by
ff
#
c1-
;'C--!-:-lr
-1 -i''r---'i- 1'-"i" :"*
l'
1
{i .+, -a-*, .,te.--*,,*,,.'4, *t, s
..: .r.---.,- -i. . :;-.14
". I
.:^r;
-
.-+,
"
t..,
tist*i4:SrS
..1 .! nr. .; '-,. ;.
i:li
i f i':
.-
,
t;,:
i i ': :l.
",; '-, t"*
..*
i'.-|
.
Tt*.b
.::.., :
'1.'
!:l:
4,.
.
/:::.
.n
ya
Ir7
:- ,\ .
"
:
'
:
:-g
,-
i
\*
'- i
',.d
1
' ;
(No v)
<q,t->
-d
\#
,,j x
d) Method #4
c) Method #3
f
#
...
t:ali
*ii....i,.'
i""{
. .-
,#
foltowed
by R'^-or,, (k'D'6'.
followed by
tf
$
-.-D:
i"c*
ir
**
#
;ra,.-,f: "*
t:
i:a
'"i.' . -i'.',
i:;
1;
i,..,.
i. . ;,.
.
i;
i-v.
.
,ti
i'i
-i";.
.
. i. .. ..*..
t'
-4-
#
13S{b&r8*
.
:N-
^r
P-: -".