Download Notes and Homework - Unit 2 Packet 2 of 5

8th Grade
Unit 2 – Geometry:
Packet 2 of 5
Mr. Rothdiener
Name: _____________________________________
Packet Outline, Page 1
 2.8: Sequences of Rigid Motions (8.G.A.2), Pages 2-5
o I can describe a sequence of rigid motion to map one figure onto another.
 2.9: Definition of Congruence and Some Basic Properties (8.G.A.2), Pages 6-9
o I can know that to prove two figures are congruent there must be a
sequence of rigid motions that maps one figure onto another.
 2.10: Angles Associated with Parallel Lines (8.G.A.5), Pages 10-13
o I can know that corresponding angles, alternate interior angles, and
alternate exterior angles of parallel lines are equal.
o I can know that when these pairs of angles are equal, then lines are
parallel.
 2.11: Angles Associated with Parallel Lines – Algebra (8.G.A.5), Pages 14-17
o I can know that corresponding angles, alternate interior angles, and
alternate exterior angles of parallel lines are equal.
o I can know that when these pairs of angles are equal, then lines are
parallel.
 2.12: Angle Sum of a Triangle (8.G.A.5), Pages 18-21
o I can know and apply the Angle Sum Theorem for triangles; the sum of
the interior angles of a triangle is always 180°.
 2.13: Exterior Angles of a Triangle (8.G.A.5), Pages 22-25
o I can write equations to find missing interior and exterior angle measures of
triangles.
 Quiz 2.2 Review (8.G.A.2, 8.G.A.5), Pages 26-27
o Given two congruent figures, I can describe a sequence that exhibits the
congruence between them.
o I can apply the facts about angle sum and exterior angles of triangles and
about angles created when parallel lines are cut by a transversal.
1
2.8: Sequences of Rigid Motions (8.G.A.2)
Bell Work:
Name a vector that will result in an inverse translation to ⃗⃗⃗⃗⃗
𝐴𝐵.
Whole-Class:
1.) In the following picture, triangle ABC can be traced onto a transparency and
mapped onto triangle A’B’C’. Describe a basic rigid motion, or sequence of,
that would map one triangle onto the other.
2.) In the following picture, triangle ABC can be traced onto a transparency and
mapped onto triangle A’B’C’. Describe a basic rigid motion, or sequence of,
that would map one triangle onto the other.
2
Guided Practice:
3.) In the following picture, triangle ABC can be traced onto a transparency and
mapped onto triangle A’B’C’. Describe a basic rigid motion, or sequence of,
that would map one triangle onto the other.
4.) Let two figures ABC and A’B’C’ be given so that the length of curved segment
AC = the length of curved segment A’C’, | < B | = | < B’ | = 80o, and | AB | = |
A’B’ | = 5. With clarity and precision, describe a sequence of rigid motions that
would map figure ABC onto figure A’B’C’.
3
Independent Practice:
5.) In the following picture, we have two pairs of triangles. In each pair, triangle
ABC can be traced onto a transparency and mapped onto triangle A’B’C’.
Describe a basic rigid motion, or sequence of, that would map one triangle onto
the other.
a)
b)
4
HOMEWORK 2.8
For numbers 1-2, describe a sequence of rigid motions that would map figure ABC
onto figure A’B’C’.
1.)
A
A’
B’
B
C
C’
2.)
A
B’
B
C
A’
5
C’
2.9: Definition of Congruence and Some Basic Properties (8.G.A.2)
Bell Work:
Fill in the blanks:
What transformation is used to bring to figures together?
Whole-Class:
Congruence is a sequence of basic rigid motions that maps one figure onto another.
1.) Describe the sequence of basic rigid motions that shows 𝑆1 ≅ 𝑆2 .
6
Guided Practice:
2.) Describe the sequence of basic rigid motions that shows 𝑆2 ≅ 𝑆3 .
Independent Practice:
3.) Describe the sequence of basic rigid motions that shows 𝑆1 ≅ 𝑆3 .
7
4.) Is △ 𝐴𝐵𝐶 ≅△ 𝐴′ 𝐵′ 𝐶 ′ ? If so, describe the sequence of rigid motions that proves
they are congruent. If not, explain how you know.
8
HOMEWORK 2.9
1) Use the diagram below the answer the following questions.
V
Q
T
R
U
S
a) Given two right triangles with lengths shown below, is there one basic rigid
motion that maps one to the other? Explain.
b) Describe the congruence that would map one triangle onto the other.
9
2.10: Angles Associated with Parallel Lines (8.G.A.5)
Bell Work:
1. An angle that is greater than 0o and less than 90o: ____________________
2. An angle that is greater than 90o and less than 1800: ____________________
3. An angle that measures 180o: _________________________
4. An angle that measures 90o: _________________________
5. Two angles whose sum is 90o: _________________________
6. Two angles whose sum is 180o: _________________________
Whole-Class:
Parallel lines – lines in a plane that never ____________________________.
Transversal – a line that ____________________ two or more lines.
Lines k and m are parallel. Line p is a transversal.
p
5
k
1
2
6
7
m
3
4
8
Alternate Interior Angles: __________________________________
Alternate Exterior Angles: _________________________________
Corresponding Angles: _____________________________________
Vertical Angles:___________________________________________
Supplementary Angles:_____________________________________
10
Guided Practice:
1.) In the diagram below, lines s and t are parallel. Use it to answer the following
problem.
1
s
2
3
4
5
t
6
7
8
The measure of <1 = 60º. Fill in the measure of each angle and its relationship to <1.
Angle
Measure
Relationship
<2
<3
<4
<5
<6
<7
<8
11
Independent Practice:
2.) Using the diagram below, identify each pair of angles as: vertical angles,
corresponding angles, alternate interior angles, alternate exterior angles, or
supplementary. a||b
7 4
1 5
6 8
3 2
a
b
a) 4 and 8______________________________
b) 7 and 3 _____________________________
c) 1 and 4 _____________________________
d) 1 and 3_____________________________
e) 5 and 6_____________________________
f) 4 and 3 _____________________________
3.) If the measure of angle 6 is 55, what other angles also measure 55?
12
HOMEWORK 2.10
1-6: Use the diagram below.
q
p
1 2
4 3
5 6
7
8
1) Name the interior angles shown. ______________________________
2) Name two pairs of alternate interior angles. _____________________________
3) Name two pairs of angles that you would describe as alternate exterior angles.
___________________________________
If p || q, classify each statement as true or false.
4) 2  8 ______
5) 3  7 ______
6) 7  1 ______
In 7 and 8, r || s and the measure of one angle is given. Find the measures of the
numbered angles.
7)
8)
1 2
4 3
5
8
1 2
4 3
r
55º
7
r
5
s
6
8
13
57º
s
2.11: Angles Associated with Parallel Lines – Algebra (8.G.A.5)
Bell Work:
Name three types of congruent angle pairs associated with two parallel lines cut by
a transversal.
Whole-Class:
1.) Given l || m
9x + 18 6x +12
l
m
A) What type of angle pair is given? _____________________
B) Write an equation to determine the measure of each angle._________________
C) Solve for x.
D) Determine the measure of each angle.
14
Guided Practice:
2.)
2x + 13
5x – 20
A) What type of angle pair is given? _____________________
B) Write an equation to determine the measure of each angle._________________
C) Solve for x.
D) Determine the measure of each angle.
3.)
1 2
3 4
5 6
7 8
A) What type of angle pair are <2 and <7? ____________________
B) If < 2 is 5x – 15, and < 7 is 3x + 15, write an equation to find x._____________
C) Solve the equation for x.
D) Find m < 2 and m < 7.
15
Independent Practice:
4-5: Find each angle in the diagram.
4.)
4x – 15
2x + 19
5.)
9y – 15
4y + 30
16
HOMEWORK 2.11
1.)
3x – 5
7x – 57
A) What type of angle pair is given? _____________________
B) Write an equation to determine the measure of each angle._________________
C) Solve for x.
D) Determine the measure of each angle.
2.)
6x – 27
2x + 13
A) What type of angle pair is given? _____________________
B) Write an equation to determine the measure of each angle._________________
C) Solve for x.
D) Determine the measure of each angle.
17
2.12: Angle Sum of a Triangle (8.G.A.5)
Bell Work:
Is ∆𝐴𝐵𝐶 ≅ ∆𝐴′𝐵′𝐶′? If so, describe the sequence of rigid motions that proves
they are congruent.
A’
A
B
B’
C
C’
1-10: Find the measure of each angle.
Whole-Class:
1.)
2.)
450
670
750
530
18
Guided Practice:
3.)
4.)
x
680
x
230
310
530
5.)
x
6.)
300
x
220
x + 53
2x + 27
19
Independent Practice:
7.) m < E = 1180, m < R = 260, Find < H.
8.) m < O = 470, m < G = 430, Find < H.
H
O
H
E
R
G
9.)
x
x
10.)
2x – 12
x
20
HOMEWORK 2.12
Find the measures of each of the angles of the triangle.
1.)
2.)
83o
3.)
61
72o
xo
o
xo
4.)
x
(x + 5)
o
85
5.)
2x
7x
(2x + 15)
21
48o
29o
xo
27o
2.13: Exterior Angles of a Triangle (8.G.A.5)
Bell Work:
State what you learned about the sum of the angles of a triangle.
Whole-Class:
Use the diagram below to complete Exercises 1–4.
1) Name an exterior angle and the related remote interior angles.
2) Name a second exterior angle and the related
remote interior angles.
3) Name a third exterior angle and
the related remote interior angles.
4) Show that the measure of an exterior angle is equal to the sum of the related
remote interior angles.
22
Guided Practice:
5) Find the measure of angle x.
6) Find the measure of angle x.
7) Find the measure of each angle.
8x – 15
3x + 20
4x + 5
23
Independent Practice:
8) Find the measure of angle x.
9) Find the measure of angle x.
10) Find the measure of each angle.
78
4x
x–3
24
HOMEWORK 2.13
For each of the problems below, use the diagram to find the missing angle
measure(s). Show your work.
1)
2)
3)
4)
25
Quiz 2.2 Review
(8.G.A.2, 8.G.A.5)
Use your knowledge of math to complete each of the following questions. Show
your work!
1.) Describe a sequence of rigid motions that would prove the congruence.
B
C’
B’
A’
C
A
 _____________________________________________________________

_____________________________________________________________

_____________________________________________________________
2.)
3x + 27
7x – 25
A) What type of angle pair is given? _____________________
B) Write an equation to determine the measure of each angle._________________
C) Solve for x.
D) Determine the measure of each angle.
26
3.) Find the measure of the missing angle.
89o
56o
xo
4.) Find the measures of each of the missing angles.
x
(x + 7)
93
o
5.) Find the measure of the missing angle.
27