2 Chapter Review
Vocabulary Help
Review Key Vocabulary
congruent figures, p. 44 translation, p. 50 angle of rotation, p. 62
corresponding angles, p. 44 reflection, p. 56 similar figures, p. 72
corresponding sides, p. 44 line of reflection, p. 56 dilation, p. 84
transformation, p. 50 rotation, p. 62 center of dilation, p. 84
image, p. 50 center of rotation, p. 62 scale factor, p. 84
Review Examples and Exercises
2.1 Congruent Figures (pp. 42–47)
Trapezoids EFGH and QRST F 5 ft G R S
are congruent. 4 ft
3 ft
E 8 ft H Q T
a. What is the length of side QT ? b. Which angle of QRST corresponds to ∠H ?
Side QT corresponds to side EH.
So, the length of side QT is 8 feet. ∠ T corresponds to ∠ H.
Use the figures above.
1. What is the length of side QR ? 2. What is the perimeter of QRST ?
The figures are congruent. Name the corresponding angles and the
corresponding sides.
3. A K 4. Q R W X
C B M L
T S Z Y
2.2 Translations (pp. 48 –53)
Translate the red triangle 4 units left and 1 unit down. What are the coordinates
of the image?
Move each vertex 4 units y
A
left and 1 unit down.
AŁ
BŁ B
Connect the vertices. C
Label as AŁ, BŁ, and CŁ. CŁ1 2 3 4 5 6 x
The coordinates of the image are A′(−1, 4), B′(2, 2), and C ′(0, 0).
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Tell whether the blue figure is a translation of the red figure.
5. 6.
7. The vertices of a quadrilateral are W(1, 2), X(1, 4), Y(4, 4), and Z(4, 2). Draw the
figure and its image after a translation 3 units left and 2 units down.
8. The vertices of a triangle are A(−1, −2), B(−2, 2), and C(−3, 0). Draw the figure
and its image after a translation 5 units right and 1 unit up.
2.3 Reflections (pp. 54–59)
The vertices of a triangle are A(−2, 1), B(4, 1), and C(4, 4). Draw the figure and its
reflection in the x-axis. What are the coordinates of the image?
y C
Points A and B are 1 4
unit above the x-axis. 3 Point C is 4 units
above the x-axis.
A B
Ź3 AŁ O 1 2 3 4 5 x
Plot points AŁ and BŁ BŁ
1 unit below the x-axis. Plot point CŁ 4 units
Ź3 below the x-axis.
Ź4
CŁ Connect the vertices.
The coordinates of the image are A′(−2, −1), B′(4, −1), and C′(4, −4).
Tell whether the blue figure is a reflection of the red figure.
9. 10.
Draw the figure and its reflection in (a) the x-axis and (b) the y-axis.
11. A(2, 0), B(1, 5), C(4, 3) 12. D(−5, −5), E(−5, −1), F(−2, −2), G(−2, −5)
13. The vertices of a rectangle are E(−1, 1), F(−1, 3), G(−5, 3), and H(−5, 1).
Find the coordinates of the figure after reflecting in the x-axis, and then
translating 3 units right.
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2.4 Rotations (pp. 60–67)
The vertices of a triangle are A(1, 1), B(3, 2), and C(2, 4). Rotate the triangle 90°
counterclockwise about the origin. What are the coordinates of the image?
Use a similar method to y
C
plot points BŁand CŁ. 4 Draw ABC.
BŁ
3
Connect the vertices.
CŁ 90í B
Plot AŁso that segment OA and AŁ A
segment OAŁ are congruent and Ź5 Ź4 Ź3 Ź2 O 1 2 3 x
form a 90í angle.
The coordinates of the image are A′(−1, 1), B′(−2, 3), and C′(−4, 2).
Tell whether the blue figure is a rotation of the red figure about the origin.
If so, give the angle and the direction of rotation.
14. y 15. y
3 3
2 2
1
Ź4 O 4 x Ź4 Ź2 O 1 2 3 4 x
Ź2
Ź3 Ź3
The vertices of a triangle are A(−4, 2), B(−2, 2), and C(−3, 4). Rotate the
triangle about the origin as described. Find the coordinates of the image.
16. 180° 17. 270° clockwise
2.5 Similar Figures (pp. 70 –75)
a. Is Rectangle A similar to Rectangle B? Rectangle A
Rectangle B
Each figure is a rectangle. So, corresponding
4 2
angles are congruent. Check to see if
corresponding side lengths are proportional. 5
10
Length of A 10 Width of A 4
—=—=2 —=—=2 Proportional
Length of B 5 Width of B 2
So, Rectangle A is similar to Rectangle B.
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b. The two rectangles are similar. Find x.
Because the rectangles are similar, corresponding side lengths are proportional.
So, write and solve a proportion to find x.
10 m
10 4
—=— Write a proportion. 4m
24 x
10x = 96 Cross Products Property 24 m
x = 9.6 Divide each side by 10.
x
So, x is 9.6 meters.
Tell whether the two figures are similar. Explain your reasoning.
18. 19. 42
10 8 12
6 5
8 8 28 28
6
7 6
21
The figures are similar. Find x.
20. 21.
20 in. x 6 cm x
14 in. 7 in.
4 cm
6 cm
2.6 Perimeters and Areas of Similar Figures (pp. 76–81)
a. Find the ratio (red to blue) of the perimeters of the similar parallelograms.
Perimeter of red parallelogram 15 15
——— = — 9
Perimeter of blue parallelogram 9
5
=—
3
5
The ratio of the perimeters is —.
3
b. Find the ratio (red to blue) of the areas of the similar figures.
3
Area of red figure
—— = —
Area of blue figure () 3 2
4
4
9
=—
16
9
The ratio of the areas is —.
16
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The two figures are similar. Find the ratios (red to blue) of the perimeters and
of the areas.
22. 23. 28 m
16 m
6m 8m
24. PHOTOS Two photos are similar. The ratio of the corresponding side lengths is
3 : 4. What is the ratio of the areas?
2.7 Dilations (pp. 82–89)
Draw the image of Triangle ABC after a dilation with a scale factor of 2.
Identify the type of dilation.
Multiply each x- and y
6
y-coordinate by the Vertices of Vertices of 5
scale factor 2. (2x, 2y) BŁ CŁ
ABC A′B′C′ 4
⋅ ⋅
3 AŁ
A(1, 1) (2 1, 2 1) A′(2, 2) B
2
(2 ⋅ 1, 2 ⋅ 2)
C
B(1, 2) B′(2, 4) 1
A
C (3, 2) (2 ⋅ 3, 2 ⋅ 2) C ′(6, 4) O 1 2 3 4 5 6 x
The image is shown at the above right. The dilation is an enlargement because
the scale factor is greater than 1.
Tell whether the blue figure is a dilation of the red figure.
25. 26.
The vertices of a figure are given. Draw the figure and its image after a
dilation with the given scale factor. Identify the type of dilation.
27. P(−3, −2), Q(−3, 0), R(0, 0); k = 4
1
28. B(3, 3), C(3, 6), D(6, 6), E(6, 3); k = —
3
29. The vertices of a rectangle are Q(−6, 2), R(6, 2), S(6, −4), and T(−6, −4).
3
Dilate the rectangle with respect to the origin using a scale factor of —.
2
Then translate it 5 units right and 1 unit down. What are the coordinates
of the image?
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