Download Geometry 2H Name: Similarity Part I

Geometry 2H
Name: ______________________________________
Similarity Part I - REVIEW
Period:
G-CO.2. Learning Target: I can represent
transformations in the plane; describe transformations as
functions that take points in the plane as inputs and give
other points as outputs. I can compare transformations
that preserve distance and angle to those that do not (e.g.,
translation versus horizontal stretch).
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2
3
4
5
6
7
8
G.CO-10. Learning Target: I can prove that the segment
joining midpoints of two sides of a triangle is parallel to
and half the length of the third side.
2. The coordinates of the vertices of a triangle are
𝐾(2,4), 𝐿(−2, −2), and 𝑀(4, −2).
1. Use the triangle below,
R
T
(a) Find the midpoint of KL and LM . Label them R and
T.
 2  (2) 4  (2) 
R
,
   0,1
2
2


 2  4 2  (2)   2 4 
T 
,
   ,   1, 2 
2
 2
 2 2 
(a) What are the coordinates of ∆𝐴′ 𝐵′ 𝐶 ′ , which is the
image of ∆𝐴𝐵𝐶 under the transformation
(x, y)  (y, - x)
𝐴′ : (-2, 6)
_𝐵′ : (6, 1)
___ 𝐶′:(1, -2)
(b) Calculate the slopes of RT and KM .
Explain how the lengths of the sides AND the
measurements of the angles for this triangle compare
with the original triangle.
The length of the corresponding sides and the
corresponding angles are congruent because the two
triangles are congruent by the rotation of 90 CW
about the origin.
mKM
(c) Calculate the lengths of RT and KM .
(b) What are the coordinates of ∆𝐴′ 𝐵′𝐶 ′ , which is the
image of ∆𝐴𝐵𝐶 (use the original figure again) under the
transformation (𝑥, 𝑦)  (2𝑥, 3𝑦)?
𝐴: (-12, -6)
𝐵′ : (-2, 18)
2  1 3

 3
1 0
1
4   2  6


 3
24
2
mRT 
RT 
1  0   2  1
2
2
1   3

2
2
 1 9
RT  10  3.2
_ 𝐶 ′ : (4, 3)
KM 
Explain how the lengths of the sides and the
measurements of the angles for this triangle compare
with the original triangle.
The transformation is not a dilation so the
corresponding side lengths are not proportional and
the corresponding angles are not congruent.
 4  2   2  4
2
2

 2   6
2
2
 4  36
KM  40  2 10  6.3
(d) Using your calculations from (a), (b), and (c), explain
the relationship between RT and KLM .
RT is the midsegment of the KLM.
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Geometry 2H: Similarity Part I - REVIEW
Name: ______________________________________
G-SRT.1. Learning Target: I can verify the following
statements by making multiple examples: a dilation of a
line is parallel to the original line if the center of dilation
is not on the line; a dilation of a line segment changes the
length by a ratio given by the scale factor.
4. Given the segment shown below. If it is dilated about
Point U, complete the following statements:
3. Graph ̅̅̅̅
𝐷𝐸 with 𝐷(−3, 6) and 𝐸(6, −6) on the
coordinate plane below.
̅̅̅̅ using the origin as the center
(a) Graph the dilation of 𝐷𝐸
and a scale factor of
1
. Label the dilation ̅̅̅̅̅̅
𝐷 ′ 𝐸 ′.
3
D
D’
E’
(a). The slopes of the segments will be
____same____________, so the segments will be
(reciprocal, same, different– choose one )
____parallel______________
E
(parallel, perpendicular, coinciding – choose one)
(b) The segments will be __similar___________
(b) Are the two segments parallel, perpendicular,
coinciding, or none of the above? _Parallel______
(c) Find the length of the DE and D ' E ' .
DE 
 3  6   6  (6) 
2
2
 9   12 

2
 81  144
2
DE  225  15
D'E ' 
 1  2   2  (2) 
2
2

 3   4 
2
2
 9  16
D ' E '  25  5
(d) Find the value of the ratio of the length of the dilated
segment to the length of the original segment.
1
3
(congruent, similar, neither – choose one)
because dilation produce similar figures.
Geometry 2H: Similarity Part I - REVIEW
G-SRT.2.Learning Target: I can decide if two figures are
similar based on similarity transformations. I can use
similarity transformations to explain the meaning of
similar triangles as the equality of all corresponding pairs
of angles and the proportionality of all corresponding
pairs of sides.
Name: ______________________________________
7. Are the two triangles shown below similar? If so,
explain why and provide a similarity statement. If not,
explain why. Show all of your work.
5. Are the two triangles below similar? If so, explain why
and provide a similarity statement. If not, explain
why. Show all of your work.
No, the triangles are
not similar since the corresponding sides length are not
proportion.
7 14
1 14

 
28 39
4 39
No, the triangles are not similar since the corresponding
sides length are not proportion..
8. For each of the following, explain whether the
following triangles are similar and provide a
similarity statement, or not similar and why.
6 9 12
3 3 1


  
8 12 24
4 4 2
6. Are the two triangles shown below similar? If so,
explain why and provide a similarity statement. If not,
explain why. Show all of your work.
Yes the triangles are similar by SAS similarity postulate.
ABC  DBC by vertical angle, corresponding sides
are proportion by the scale factor of
G-SRT.3 Learning Target: I can establish the AA
criterion by looking at multiple examples using similarity
transformation of triangles.
2
.
3
18 24
2 2

 
27 36
3 3
R  S by alternative interior angles theorem
RMP  SMQ by vertical angles theorem
(a)
Yes, the triangles are similar by
AA Similarity Theorem.
R  S by AIA theorem
RMP  SMQ by vertical
angles theorem
PRM  QMS
(b)
Yes, the triangles are similar by
AA Similarity Theorem.
A  A by Reflexive Property
ABC  ADE by
corresponding angles postulate.
ABC  ADE
(c)
No the triangles are not similar
by AA Similarity Theorem
since it only have one pair of
congruent angle M  Q
R
P
M
Q
S
D
B
A
E C
R
P
M
S
Q