Are You Ready?
8th Grade Pre-Algebra Chapter 13
Calculators Allowed
Vocabulary
1.) Complementary angles:
2.) Supplementary angles:
3.) Vertical angles:
4.) Transversal:
List the following angle pairs using the diagram:
5.) Corresponding angles:
6.) Alternate interior angles:
7.) Alternate exterior angles:
8.) Transformation:
9.) Image:
10.)
Translation:
11.)
Reflection:
12.)
Line of symmetry:
13.)
Rotation:
14.)
Dilation:
15.)
Scale factor:
Name:
Date:
Block:
Tell whether the angles are complementary,
supplementary, or neither.
16. 𝑚∠87⁰
𝑚∠93⁰
a. complementary
b. supplementary
c. neither
17. 𝑚∠25⁰
𝑚∠67⁰
a. complementary
b. supplementary
c. neither
18. 𝑚∠102⁰
𝑚∠88⁰
a. complementary
b. supplementary
c. neither
23.
𝑥 = ________
(5𝑥 + 35)⁰
45⁰
∠ = ________
Tell whether the angles in the diagram are
corresponding, alternate interior, or alternate
exterior angles.
Find the angle measure.
19. ∠1 and ∠2 are supplementary and 𝑚∠1 = 48⁰
𝑚∠2 = _________
20. ∠3 and ∠4 are complementary and 𝑚∠3 = 72⁰
24. ∠1 & ∠7
a. corresponding
b. alternate interior
c. alternate exterior
25. ∠3 & ∠5
a. corresponding
b. alternate interior
c. alternate exterior
26. ∠4 & ∠8
a. corresponding
b. alternate interior
c. alternate exterior
𝑚∠2 = _________
Find the measures of the numbered angles.
21.
𝑚∠1 = ______
145⁰
1
3
2
𝑚∠2 = ______
𝑚∠3 = ______
Lines r and t are parallel.
Find the measure of the angles listed below.
Find the value of x in the figure. Then find the
unknown angle measures.
22.
27.
1
110⁰
2 3
4
(2𝑥 + 60)⁰
𝑥 = ________
(5𝑥)⁰
𝑚∠1 = ______
∠ = ________
𝑟
5
6 7
7
𝑚∠4 = ______
𝑚∠2 = ______
𝑚∠5 = ______
𝑚∠3 = ______
𝑚∠6 = ______
𝑡
𝑚∠7 = ______
28. Find the value of 𝑥.
𝑥 = ________
(2𝑥 + 60)⁰
Graph the polygon. Then graph its image using
the indicated reflection.
33. 𝐴 (−4, 2), 𝐵 (−1, 2), 𝐶 (−5, 4); 𝑥 − 𝑎𝑥𝑖𝑠
y
5
120⁰
𝐴’ (
)
𝐵’ (
)
𝐶’ (
)
4
3
2
29. Find the value of 𝑥.
1
𝑥 = ________
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
(9𝑥 + 81)⁰
–4
–5
34. 𝑇(−4, 1), 𝑈 (−4, −3), 𝑉 (−1, −1); 𝑦 − 𝑎𝑥𝑖𝑠
135⁰
y
5
4
30. Find the sum of the measure of the interior
angles of the polygon: 19-gon
𝑇’ (
)
𝑈’ (
)
𝑉’ (
)
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
31. Find the measure of one angle of the
polygon: 23-gon
–3
–4
–5
Graph the polygon. Then graph its image using
the indicated translation.
32. 𝑃 (2, 3), 𝑄 (0, 0), 𝑅 (3, −2) (𝑥, 𝑦) → (𝑥 + 2, 𝑦 − 3)
How many lines of symmetry does the figure
have?
35.
_________
36.
_________
y
5
4
𝑃’ (
)
𝑄’ (
)
𝑅’ (
)
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
Draw the polygon. Then find the coordinates of
the vertices of the image under the specified
rotation, and draw the image.
Find the scale factor.
40.
37. 𝐴 (3, 4), 𝐵 (−1, 2), 𝐶 (3, 0); 90° 𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒
y
5
4
𝐴’ (
)
𝐵’ (
)
𝐶’ (
)
3
2
̅̅̅̅ with endpoints 𝐶(3, −1) and
41. Given 𝐶𝐷
𝐷(−1, 0), let ̅̅̅̅̅̅
𝐶’𝐷’ with endpoints 𝐶’(6, −2) and
𝐷’(−2, 0) be the image of ̅̅̅̅
𝐶𝐷 after a dilation.
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
38. 𝐴 (5, −4), 𝐵 (2, −2), 𝐶 (4, 1); 90° 𝑐𝑜𝑢𝑛𝑡𝑒𝑟 − 𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒
y
of
5
Draw ΔABC with the given vertices
Then find the coordinates of the vertices
of the image after a dilation having the
given scale factor and draw the image.
4
3
𝐴’ (
)
𝐵’ (
)
2
y
1
–5
–4
–3
–2
1
42. 𝐴(8, −2), 𝐵(−6, −2), 𝑎𝑛𝑑 𝐶(0, −10); 𝑘 = 2
–1
–1
1
2
3
4
5
10
x
𝐶’ (
–2
𝐴’ (
)
𝐵’ (
)
𝐶’ (
)
8
)
6
4
–3
2
–4
–5
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
39. 𝐴 (−5, −5), 𝐵 (−5, −1), 𝐶 (−1, 0); 180°
y
–8
𝐴’ (
)
𝐵’ (
)
5
4
–10
43.𝐴(−5, −2), 𝐵(−1, −2), 𝑎𝑛𝑑 𝐶(−3, −5); 𝑘 = 2
y
3
𝐶’ (
2
10
)
8
1
6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
4
𝐵’ (
)
𝐶’ (
)
2
–3
–5
)
x
–2
–4
𝐴’ (
–10 –8
–6
–4
–2
–2
–4
–6
–8
–10
2
4
6
8
10
x
Draw the polygon shown. Then find the coordinates of the vertices of the final image after the specified
transformations, and draw the final image.
44.) Reflect the polygon in the y-axis, then
rotate the image 90° clockwise
45.) Translate the polygon (𝑥, 𝑦) → (𝑥 + 5, 𝑦 − 1),
then reflect the image in the x-axis
46.) Rotate the polygon 180°, then dilate the
47.) Translate the polygon (𝑥, 𝑦) → (𝑥 − 6, 𝑦 + 1),
then rotate the image 90° counterlcockwise
image 𝑘 =
1
2
Applications
Answer the following questions showing ALL WORK necessary! Be sure to
label your answer when necessary.
1
48.) ΔABC was dilated with a scale factor 𝑘 = 3
a.) Find the area of ΔABC
b.) Find the area of ΔA’B’C’
c.) What is the ratio of the original figure’s area to the image’s area?
Writing
Answer the following questions in complete sentences. Be sure to use
examples and correct math terminology when possible.
49.) After which transformation(s) is a polygon and its image congruent?
50.) If a figure is in Quadrant I and is rotated 90° counter-clockwise, where will the image be located?