1. 1. Given RST XYZ with ~ RS XY ST YZ 3 2 RT XZ
= = Find 3 2
ANSWER
2. Given EFG MNP with ~ EF MN 2 1
= If FG = 4.5, find NP.
ANSWER
2.25

2. EXAMPLE 1
Describe a dilation
FEG is similar to FDH. Describe the dilation that moves FEG onto FDH.
SOLUTION
The figure shows a dilation with center F.
The scale factor is 2 because the ratio of FH to FG is 20 : 10, or 2 : 1.

3. EXAMPLE 2
Describe a combination of transformations
ABC is similar to FGE. Describe a combination
of transformations that moves ABC onto FGE.
SOLUTION
A dilation with center B and scale factor moves ABC onto DBE.
Then a rotation of DBE with center E moves DBE onto FGE. The angle of rotation is equal to the measure of C. 2 3

4. GUIDED PRACTICE
for Examples 1 and 2
The two figures are similar. Describe the transformation(s) that move the blue figure onto the red figure. 1. 2.
ANSWER
ANSWER 2 3
dilation with center
B and scale factor
dilation with scale factor
and reflection 7 3

5. EXAMPLE 3
Use transformations to show figures are not similar
Use transformations to explain why ABCDE and KLQRP are not similar.

6. EXAMPLE 3
Use transformations to show figures are not similar
SOLUTION
Corresponding sides in the pentagons are proportional with a scale factor of 2 3
However, this does not necessarily mean the pentagons are similar.
A dilation with center A and scale
factor moves ABCDE onto
AFGHJ. Then a reflection moves AFGHJ onto KLMNP. 2 3
KLMNP does not exactly coincide with KLQRP, because not all of the corresponding angles are congruent. (Only A and K are congruent.) Since angle measure is not preserved, the two pentagons are not similar.

7. EXAMPLE 4
Use similar figures
GRAPHIC DESIGN A design for a party mask is made using all equilateral triangles and a scale factor of 1 2
a. Describe transformations that move triangle A onto
triangle B. b.
Describe why triangles C and D are similar by using the given information.

8. EXAMPLE 4
Use similar figures
SOLUTION
The figure shows a dilation with scale factor
followed by a clockwise rotation of 60°. 1 2 b.
Triangles C and D are similar because all pairs of corresponding sides are proportional with a ratio of
and all pairs of corresponding angles of equilateral triangles have the same measure. 1 2

9. GUIDED PRACTICE
for Examples 3 and 4
Refer to the floor tile designs shown below. In each design, the red shape is a regular hexagon.

10. GUIDED PRACTICE
for Examples 3 and 4 3.
Tile design 1 is made using two hexagons. Explain why the red and blue hexagons are not similar. 4.
Tile design 2 is made using two similar geometric shapes. Describe the transformations that move the blue hexagon to the red hexagon. 5.
Tile design 3 shows congruent angles and sides. Explain why the red and blue hexagons are similar, using the given information. 6.
If the lengths of all the sides of one polygon are proportional to the lengths of all the corresponding sides of another polygon, must the polygons be
similar? Explain.

11. GUIDED PRACTICE
for Examples 3 and 4
SAMPLE ANSWER 3.
The red hexagon has all sides congruent, but the blue hexagon has 3 shorter sides and 3 longer sides, so ratios of corresponding side lengths are not constant. 4.
dilation followed by a rotation of 30° about the center of the figures 5.
All angles are congruent, so angle measure is preserved, and all side lengths are congruent in each hexagon, so the ratio of any two corresponding side lengths is constant. 6.
No; even though corresponding sides might be proportional, if corresponding angles are not congruent, the polygons are not similar.

12. Daily Homework Quiz
Describe the dilation that moves the smaller figure onto the larger figure. 1.
ANSWER
dilation with scale factor 3 and center at the intersection of the thin lines

13. Daily Homework Quiz
Describe the dilation that moves the smaller figure onto the larger figure. 2. 8 5
ANSWER
dilation with scale factor and center at center of the circles

14. Daily Homework Quiz
The coordinates of the vertices of a ABC and its image DEF are given. Describe the transformation(s) that move ABC figure onto DEF.
A(1, 1), B(–2, 2), C(2, 2);
D(2, –2), E(–4, –4), F(4, –4)
SAMPLE ANSWER
dilation with center (0, 0) and scale factor 2, then reflection in the x-axis