similarity practice - washingtonville central school district · order on a line so that ab = 2bc =...
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G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 1
Name: __________________________________________________________ Date: __________________
Similarity
Practice
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 2
I will know how to identify corresponding angles and
sides based on similarity statements.
I will know how to develop and write similarity
statements for two polygons.
I will know how to find missing measurements in similar
polygons.
I will know how to determine if two triangles are similar
based on their corresponding parts.
I will know how to establish a sequence of similarity
transformations between two similar polygons.
I will know how to prove two triangles are similar by AA,
SAS, and SSS criteria.
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 3
1. Solve each proportion using cross products.
a) b) c) d) 3
5 15
x
x = _______
1 6
15x x
x = _______
20 6
4
x
x
x = _______
4 2
12 2 13
x
x
x = _______
e) f) g) h) 1 1
6
x x
x
x = _______
3 9
4 7x
x = _______
9 2
5
x
x
x = _______
4
5 16
x
x = _______
2. Solve the following problems. (Show work)
a) The ratio of seniors to juniors in the Chess Club is 2:3. If there are 24 juniors, how many seniors are in the club?
b) A picture is 3 in. wide by 5 in. high was enlarged so that the width was 15 inches. How high is the enlarged picture?
c) A triangle’s three angles are in the ratio of 5:7:8. What is the measure of the smallest angle?
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 4
3. What would be the best (most specific) name for the shape that has the following ratios for its SIDES.
a) 3 : 4 : 3 _________________________ b) 4 : 5 : 4 : 5 ______________ or _____________ c) 3 : 3 : 5 : 5 _________________________ d) 5: 5: 5: 5 ______________ or _____________
4. What would be the best (most specific) name for the shape that has the following ratios for its ANGLES.
a) 3 : 4 : 3 _________________________ b) 4 : 5 : 4 : 5 ______________ or _____________ c) 2 : 2 : 7 : 7 _________________________ d) 4 : 4 : 4 : 4 ______________ or _____________
5. Solve the following problems. (Show work)
a) The ratio of two supplementary angles is 4:5. Find the measures of each angle.
b) A 3 foot stick is broken into two pieces. The ratio of the two pieces is 5:7. How big are the two pieces?
c) Points A, B, C, and D are placed in alphabetical order on a line so that AB = 2BC = CD. What is the ratio BD : AD?
d) Two numbers are in ratio 7 : 3. The sum of the two numbers is 36. What is the largest number?
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 5
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. T or F b) Rotation is a similarity transformation. T or F c) All transformations are isometric. T or F d) Dilation is a non-isometric transformation. T or F e) Stretch is not a similarity transformation. T or F
4. Given that AFG DRH. Complete the following.
H ______ DR DH
AF ______ D ______
AG
RH DH ______
5. Pentagon ABCDE is similar to Pentagon RYMNT. Complete the following.
C ______ AB ED
RY ______
MN CD
RT ______
T ______ NT RT
DE ______
AB RY
BC ______
6. ABC is similar to another triangle. Provided is some information about the two triangles, BC AB
DR TD . From
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) BAC __________
M
N
TR
YB
A
E
D
C
M
K
YG
R
BA
E D
C
J
T
MA
C
BO J
T
H
A
B
C
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 6
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. ____________________ followed by _________________
b) Determine two similarity transformations that
would map OBC onto GT. ____________________ followed by _________________
c) Determine two similarity transformations that would map Quad. GHIJ onto Quad. RKYT. ____________________ followed by _________________
d) Determine two similarity transformations that
would map MNT onto RFH. ____________________ followed by _________________
O
T
E
H
B C
D
G
T
O
C
B
T
Y
R
I
H
G
J
O
K
H
R
N
M
T
F
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 7
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 ____________________ followed by _________________
b) Method #2 ____________________ followed by _________________
c) Method #3 ____________________ followed by _________________
d) Method #4 ____________________ followed by _________________
P
M
C
E
D
N
P
M
C
E
D
N
P
M
C
E
D
N
P
M
C
E
D
N
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 8
1. Solve for the missing information, given that the two triangles in each question are SIMILAR.
a) b) c)
x = ___________ y = __________
x = ___________ y = __________
x = ___________ y = __________ d) e) f)
x = ___________ y = __________
x = ___________ y = __________
ABC has sides of 5,6,7
ABC DEF
DEF has sides 9, x, y
x = ___________ y = __________
2. If the three sides of a triangle are in ratio of 3:5:7 and the perimeter of the triangle is 12 cm. What is the
length of the longest side?
y
10.8
x
6
12
10
T
G
R
S
Q
y
10
x
124
8
W
T
V
X
U
α
α
o
ox
36
y
16
12
21
186
y
15x
20
W
T
V
X
U
y
20
9
5b
3b
x
o
o
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 9
3. Use the scale factor to determine the missing values.
a) LMN : LJK is 1:2 b) QNP : HRT is 2:1
x = ____________ y = __________
x = ____________ y = __________
4. Use the Pythagorean Theorem to help you on these. Solving for the missing values.
a) b)
x = ___________ y = __________
Right ABC has sides of AB = 8, BC = 15, & AC = x
where AC is the hypotenuse
ABC DEF
Right DEF has sides DE = z, EF = y, & DF = 51
x = ___________ y = __________ z = ___________
y
3
x
4
o
o
M
J
L
K
N
Y
X
24
21
20°20°
P
Q
NR
H
T
y
x
4
3
6
3
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 10
1. Prove that if two triangles have two congruent corresponding angles, then they must be similar.
Given: A P and C N Prove: ABC PMN
2. Prove that if two triangles have two corresponding proportional sides and the included corresponding
congruent angle (SAS) is enough for establishing similarity.
Given: A P and PM PN
AB AC Prove: ABC PMN
3. Prove that for two triangles to be similar we need to find a sequence of similarity transformations that map
ABC on to DEF.
Given: PM PN MN
AB AC BC Prove: ABC PMN
x
x
o
o
M
N
P
A
B
C
o
o
P
M
N
A
B
C
N
P
M
B
A
C
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 11
4. By construction, use similarity constructions to map ABC onto NMP.
(Hint: ,2BD ABC first and then reflect.) (There are many ways to do this construction)
5. By construction, use similarity construction to map ABC onto NPM.
(Hint: 1,2
BD ABC first and then rotate.) (There are many ways to do this construction)
x
o
x
o
P
N
M
A
B
C
P
M
N
A
C
B
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 12
1. Are the following pairs of triangles similar? If they are, then name their similarity criteria. (SSS, SAS, AA)
a) Yes / No __________ b) Yes / No __________ c) Yes / No __________
d) Yes / No __________ e) Yes / No __________ f) Yes / No __________
2. Are the following pairs of triangle similar? If YES, name the similarity criteria (SSS, SAS, AA)
a) Yes / No
Criteria ________
b) Yes / No
Criteria ________
c) Yes / No
Criteria ________
d) Yes / No
Criteria ________
e) Yes / No
Criteria ________
f) Yes / No
Criteria ________
g) Yes / No
Criteria ________
h) Yes / No
Criteria ________
3. Jeff asks the teacher is ASA is also a similarity criterion. The teacher says yes but it isn’t needed. Why
isn’t it needed?
o
o
5.62.8
7
3.5
8
4
60°
57°
53°
57°
20°15° θx
o
o
10
16
4
6
o
o
o
o7.54.5
5 393°
93°
16
20
15
8
6
12
o
o
9 612
8
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 13
4. Are the following pairs of triangle similar? If YES, name the similarity criteria (SSS, SAS, AA) and create a
similarity statement. If NO, just circle No.
a) Yes / No
Criteria ________
_____ _____
b) Yes / No
Criteria ________
_____ _____
c) Yes / No
Criteria ________
_____ _____
d) Yes / No
Criteria ________
_____ _____
5. Prove the following relationships.
a) GIVEN: LN = 4 cm, KL = 5 cm LY = 12 cm, LH = 15 cm
PROVE:
KLN HLY
b) GIVEN: G HIJ
PROVE:
FGH JIH
STATEMENT REASON
STATEMENT REASON
c) GIVEN: ABCD is a parallelogram
PROVE:
AHE FHG
d) GIVEN:
1 2 & AC AE
PROVE:
CBD EFD
STATEMENT REASON
STATEMENT REASON
96°
21°63°
63°
H
G
R
E
D
F
T
G
R
S
Q
o
W
T
V
X
U 8.25
4 5.5
9.9
6.64.8
P
O
N
T
R
H
12
154
5K
H
L
N
Y
o
o
F H
G
I
J
H
BA
D C
FG
E
2
1
B
A
C
E
D
F
G.SRT.A.2-3 PRACTICE WS #1-3 – geometrycommoncore.com 14
2. Prove the following relationships.
a) GIVEN: PQ PR
PT PS
PROVE:Q
b) GIVEN: U ZTW
PROVE: UV WU
TZ WT
STATEMENT REASON
STATEMENT REASON
c) GIVEN:
||AB DC
PROVE:
GA GC = GB GH
d) GIVEN: FG = 7 cm, GH = 8 cm, FH = 10 cm CB = 14 cm, BA = 16 cm, AC = 20 cm
PROVE:
F C
STATEMENT REASON
STATEMENT REASON
e) GIVEN: TH TL
TJ TK
PROVE: ||HL KJ
f) GIVEN: TUW TVX
PROVE:TU TW
TV TX
STATEMENT REASON
STATEMENT REASON
P
Q R
S To
o
W
V
U
Z
T
G
BA
D H
C20
14
16
10
87
A
C
BF
G
H
T
H
KL
J
o
o
W
T
V
X
U