Regents Exam Questions CC.G.SRT.2: Similarity
Page 1
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Name: __________________________________
CC.G.SRT.2: Given two figures, use the definition of similarity in terms of
similarity transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity for triangles as the equality of all
corresponding pairs of angles and the proportionality of all corresponding pairs of
sides.
1 The perimeter of
, the image of
, is twice as large as the perimeter of
. What type of transformation has taken place?
1) dilation
2) translation
3) rotation
4) reflection
2 A triangle is dilated by a scale factor of 3 with the center of dilation at the origin. Which
statement is true?
1) The area of the image is nine times the area
of the original triangle.
2) The perimeter of the image is nine times the
perimeter of the original triangle.
3) The slope of any side of the image is three
times the slope of the corresponding side of
the original triangle.
4) The measure of each angle in the image is
three times the measure of the corresponding
angle of the original triangle.
3 If
1)
2)
3)
4)
is dilated by a scale factor of 3, which statement is true of the image
?
Regents Exam Questions CC.G.SRT.2: Similarity
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Name: __________________________________
4 The image of
after a dilation of scale factor k centered at point A is
shown in the diagram below.
, as
Which statement is always true?
1)
2)
3)
4)
5 In the diagram below,
a dilation where
,
is the image of
,
,
Which relationship must always be true?
1)
2)
3)
4)
,
after a clockwise rotation of 180° and
, and
.
Regents Exam Questions CC.G.SRT.2: Similarity
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6 In the diagram below,
is the image of
The coordinates of the vertices are
,
The ratio of the lengths of
1)
to
,
after a dilation centered at the origin.
,
, and
.
is
2)
3)
4)
7 In the diagram below, triangles XYZ and UVZ are drawn such that
.
Describe a sequence of similarity transformations that shows
and
is similar to
.
Regents Exam Questions CC.G.SRT.2: Similarity
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1 ANS: 1
2 ANS: 1
3
4
5
6
REF:
ANS:
ANS:
ANS:
ANS:
081520geo
2
4
4
1
REF: 010505a
REF: 061516geo
REF: 081506geo
REF: 081514geo
REF: 081523geo
7 ANS:
Triangle
is the image of
after a rotation about point Z such that
coincides with
.
Since rotations preserve angle measure,
coincides with , and corresponding angles X and Y, after
the rotation, remain congruent, so
. Then, dilate
at point Z. Since dilations preserve parallelism,
REF: spr1406geo
maps onto
by a scale factor of
. Therefore,
with its center
.