1. The length of one line segment is 9cm and the length of a parallel line segment is 3cm. What scale factor would you need to use to map the first line segment onto the second line semgment?
A. 9*3=27
B. 9/3=3
C. 3/9=0.33
D. 9/9=1
2. Given the coordinates below, what is the scale factor of a dilation centered at the origin where
3. ′‾A′B′is the image of ‾AB
A(6,−4),B(2,−8)
A′(9,−6),B′(3,−12)
4. Which of the following statements is true for the image below if ↔QR is dilated by a scale factor of 3and ↔TU is dilated by a scale factor of 1/3
A. The dilated lines are perpendicular
B. The dilated line segments intersect at S but are not perpendicular.
C. The dilated lines are parallel.
D. The dilated line segments intersect at a point other than S
5. What can be concluded if one triangle maps onto another after a sequence of similarity transformations?
A. The two triangles are similar because similarity transformations produce proportional angles and congruent distances.
B. The two triangles are similar because similarity transformations preserve angle measure and produce proportional distances in a figure.
C. The two triangles are congruent because simiarity transformations preserve angle measure and distances in a figure.
D. The two triangles are not congruent because similarity transformations produce congruent angles and proportional distances.
6. Select a sequence of similarity transformations that maps one triangle onto the other.
A. a reflection followed by a rotation
B. a rotation followed by a dilation
C. a translation followed by a dilation
D. a reflection followed by a dilation
7. What transformations preserve angle measure?
A. Translation
B. Reflection
C. Rotation
D. Dilation
8. What transformations preserve distance?
A. Translation
B. Reflection
C. Rotation
D. Dilation
9. In similar triangles the corrosponding sides are---------------and the corrosponding angles are----
Proportional
Congruent
10. Are the two triangles below similar? If so, write a similarity statement and state which similarity criteria can be used to prove it?
11. Similarity Statement: ------------:
△ABC ~ △DEF
△ABC ~ △FDE
△ABC ~ △EFD
The triangles are not similar
Criteria
AA~
SAS~
SSS~
Not applicable, the triangles are not similar.
12. Identify two similar triangles in the figure below. State the criteria that proves they are similar. Finally, determine the length of ‾AB
Similar Triangles---------
△ABC ~ △ABD
△ABC ~ △ADB
△DBC ~ △ABD
△DBC ~ △ABC
Criteria
AA~
SAS~
SSS~
AB=
6
8
1. The scale factor would be 3/9=0.33 (C).
2. The scale factor of the dilation is 3/2=1.5.
3. The dilated line segments intersect at S but are not perpendicular, so the answer is B.
4. The two triangles are similar because similarity transformations preserve angle measure and produce proportional distances in a figure, so the answer is B.
5. The correct sequence of similarity transformations would be a rotation followed by a dilation, so the answer is B.
6. Translation, reflection, and rotation preserve angle measure, so the answer is A, B, and C.
7. Translation and reflection preserve distance, so the answer is A and B.
8. In similar triangles, the corresponding sides are proportional and the corresponding angles are congruent.
9. The two triangles are similar, and the similarity statement is △ABC ~ △DEF. The similarity criteria that can be used to prove it is SSS~
10. The two similar triangles are △ABC ~ △ABD and △ABC ~ △ADB. The criteria that prove they are similar is AA~. The length of AB is 6 units (given).