Download Geometry 2 Name: Similarity Part I - REVIEW Period: 1 2 3 4 5 6 7 G

Geometry 2
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).
1
2
3
4
5
6
7
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. Given ABC with vertices at A(-1,0), B(0,5), and
C(2,-1)
(a) Graph the original triangle.
(b) What are the coordinates of ∆𝐴′ 𝐵′ 𝐶 ′ , which is the
image of ∆𝐴𝐵𝐶 under the transformation
(𝑥, 𝑦)  (𝑥 − 2, 𝑦 + 3)?
𝐴′ : __________ 𝐵′ : _________
(a) Find the midpoint of KL and LM . Label them R
and T.
𝐶𝑍 ′ :_________
Explain how the lengths of the sides AND the
measurements of the angles for this triangle compare
with the original triangle.
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(b) Calculate the slopes of RT and KM .
(c) Calculate the lengths of RT and KM .
(c) 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, 2𝑦)?
𝐴: ___________ 𝐵′ : _________
𝐶 ′ : __________
Explain how the lengths of the sides and the
measurements of the angles for this triangle compare
with the original triangle.
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(d) Using your calculations from (a), (b), and (c), explain
the relationship between RT and KLM .
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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.
3. Graph ̅̅̅̅
𝐷𝐸 with 𝐷(2, −3) and 𝐸(−1, −3) on the
coordinate plane below.
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.
4. Are the two triangles below similar? If so, explain
why and provide a similarity statement. If not,
explain why. Show all of your work.
_____________________________________________
(a) Graph the dilation of ̅̅̅̅
𝐷𝐸using the origin as the center
and a scale factor of 2. Label the dilation ̅̅̅̅̅̅
𝐷 ′ 𝐸′.
(b) Calculate the slope of DE and the slope of D ' E ' .
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5. 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.
Classify the two segments as parallel, perpendicular, or
neither. ______________________
Explain your answer.
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(c) Find the length of the dilated line segment.
(d) Find the value of the ratio
D'E'
.
DE
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G-SRT.3. Learning Target: I can establish the AA
criterion by looking at multiple examples using similarity
transformation of triangles.
6. Given each of the diagrams below, explain how the
two triangles shown are similar by AA~.
(a)
Bonus Review to help you be successful…
#1 - Given that line r is parallel to line s, identify a pair of
each of the following:
- alternate interior angles
- alternate exterior angles
- corresponding angles
- vertical angles
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(b)
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(c)
#2 – The angles of a triangle all add to equal ______.
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#3 – Draw a picture (with numbers) to correctly illustrate
each of the following:
SSS~
SAS~
AA~