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Itg2 U3 Vocab
Vocabulary WS
Point
Can be thought of as a dot that
represents a location in a plane or in
space
Line *
Is understood to be straight, to contain
an infinite number of points, to extend
infinitely in two directions and has no
thickness.
Line segment *
A line with endpoints, thus its length is
measurable.
Ray *
Consist of an initial point and all the
points on a line to one side only. (
=
ray BA)
(ray AB)
Itg2 U3 WS 1 (Practice 68)
Write the name of each figure
1.
Line TG =
2.
Angles: L GHI and L IHG
3.
Plane
Can be thought of as a flat surface that
extends infinitely in all directions.
Collinear
Points, segments, or rays that are on
the same straight line are collinear.
Intersect
Where objects cross / meet.
Planes -> Line
Lines -> Point
Endpoints
The end of a line, ray, or segment.
Points where you begin and end.
Angle *
Consist of two different rays that have
the same initial point. (The initial point
is the vertex of the angle).
Two rays that have a common
endpoint.
Vertex
The initial point where the two rays
meet to make an angle.
The point where two rays intersect.
Ray QZ =
Use the following picture to answer the questions 4-6
4.
Name all the rays which have M as an endpoint.
Rays MX, MV, MY, MW =
5.
Name an angle formed by
Angle: L VMY
6.
Give two different names for L 1
Angles: L XMW and L WMX
------------------------------------------Give three different names for line l below.
Lines: AB, BC and AC =
7.
and
.
8.
Explain why the symbols
and
represent the
same geometric figure.
Segments are measurable and have a starting and
ending point so these lengths are the same.
9.
Explain why the symbols
and
do not
represent the same geometric figure.
Segment
is measurable, whereas line
goes on forever.
Itg2 U3 WS 2 (Practice 69)
Use a protractor to measure each angle
1.
115o
2.
7.
68o
8.
136o
9.
Draw angle QMN, which has a measure of 140o
90o
10. Draw angle XYZ, which has a measure of 46o
3.
25
o
11. Use a protractor to measure L APY and L RPX .
How do the compare?
Use the following picture to answer the following question
m
L APY = 120 o and the m L RPX = 120 o.
These two vertically opposite angles are congruent.
4. Find the measures (in degrees) of the following angles:
(a) angle AFB 45 o (d) angle EFD 40 o
(b) angle EFB 135 o (e) angle AFD 140 o
(c) angle AFC 80 o
Use a protractor to draw an angle of the measure.
5.
170 o
6.
80 o
Itg2 U3 WS 3 (Practice 70)
Tell whether two angles with the given measures are
complementary, supplementary, or neither.
1.
80o, 10o
complementary
o
o
2.
112 , 68
supplementary
3.
43o, 137o
supplementary
4.
44o, 36o
neither
o
o
5.
138 , 42
supplementary
6.
63o, 27o
complementary
7.
114o, 96o
neither
o
o
8.
18 , 72
complementary
9.
5o, 185o
neither
Find the measure of a complement of an angle of the
given measure.
10. 53o
37o
11. 77o
13o
o
12. 15
75o
13. 84o
6o
o
14. 26
64o
o
15. 62
28o
16. 33o
57o
o
17. 19
71o
L TOP
108o
19.
L SOQ
108
o
20.
L TOQ
72o
21.
Find the measure of a complement of
L Y.
32o
22.
Find the measure of a supplement
of L Y.
148o
43.
If m L 1 = 38o and m L 2 = 52o, what can you
conclude about L 1 and m L 2?
The two angles are complementary.
Acute
44.
Obtuse
Acute
45.
Right
Find the value of x in each situation below. Pictures are
not drawn to scale, do not use a protractor.
46. x + 115 = 180
47.
x + 72 = 180
x = 65 o
x = 108 o
48.
Find the measure of L ABD in the figure below.
26 o
32.
42.
Straight
Find the measure of a supplement of an angle of the
given measure.
23. 27o
153o
o
24. 94
86o
25. 114 o
66o
o
26. 166
14o
27. 81 o
99o
o
28. 135
45o
o
29. 19
161o
30. 30 o
150o
31.
Identify each angle below as acute, obtuse, right,
or straight.
41.
Give the measure of each angle.
18.
Define each of the following.
32. Acute angle
An angle with a measure less than
90 o.
33. Obtuse angle
An angle with a measure greater
than 90 o.
34. Right angle
An angle with a measure equal to
90 o.
35. Straight angle
An angle with a measure equal to
180 o.
36. Vertical angles
Angles on opposite sides of an X.
Their measures are equal
37. Complementary
Two angles are complementary if
the sum of their measures is 90 o.
38. Supplementary
Two angles are supplementary if
the sum of their measures is 180 o
39. Adjacent angles
Two angles are adjacent if they
share a common vertex and side.
40. Linear pair
Two adjacent angles that are
supplementary
50.
2x + 98 = 180
x = 41
5x – 8 = 32
x=8
49.
x = 137
51.
4x – 25 = 35
x = 15
Itg2 U3 WS 4 (Practice 71)
1. Find the value of x and the measure of each angle.
2.
3.
4.
5.
4x + 1 = 65
L AEC and L DEC = 115 o
x= 16
L AED and L CEB = 65 o
LABC is complementary to LCBD. Sketch a picture,
and write an equation to solve for x if m LABC = 4x
and LCBD = 5x
4x + 5x = 90 o
x = 10
LABC is supplementary to LCBD. Sketch a picture
and write an equation to solve for x if L ABC = 4x and
LCBD = 5x
4x + 5x = 180 o
x = 20
LABC is a vertical angle to LDBE. Sketch a picture
and write an equation to solve for x if LABC = 4x - 20
and LDBE = 2x + 40
4x + 5x = 90 o
x = 10
Solve for x.
* Move 33 to lower left corner (corresponding). Next set
33 = to 2x – 7 (vertical angle). 2x – 7 = 33; x = 20
6.
Solve for x.
11x – 20 = 8x – 14; x = 2
7.
Solve for x.
* Move 10x – 20 to lower right corner (corresponding).
Next: 10x – 20 + 2x + 20 = 180 (Linear Pair); x = 15
8.
Solve for x.
* Move 20x – 10 to lower corner
(corresponding). Next: 20x – 10 +
10x + 10 = 180 (Linear Pair); x = 6
9.
In the figure below,
and L 4 = 110o.
Find the measure of each angle.
10. In the figure below,
,
Find the measure of each angle.
and L 2 = 120o.
11. Given that L 1 = 53o, L 3 = 140o and A || X. Find the
measure of each angle.
12. Given: L1 || L2; L4 || L5; L3  L2 and L 3 = 40o,
and L 1 = 20o , solve all other angles.
Itg2 U3 WS 5
1. Describe the measure of each of the following angles.
(a) Acute An angle measure < 90 degrees.
(b) Right An angle measure = 90 degrees.
(c) Obtuse An angle measure > 90 degrees.
(d) Straight An angle measure = 180 degrees.
8.
Solve for x.
9.
Solve for x.
2. Given the figure below.
10. Solve for y.
11.
(a) State two straight angles
(b) State two acute angles
(c) State two obtuse angles
(d) State one right angle
ABC, BED
ADB, ADC
ABD, CED
ACD
3. Given the following choices for the figure below:
(Vertical Opposites, Linear Pair, Supplementary,
Complementary and Right angle), state all choices
that apply to the following.
(a) Angles 3 & 4
(b) Angles 1 & 3
(c) Angle 5
(d) Angles 1 & 4
(e) Angles 2 & 4
4. Solve for x.
5. Solve for x.
6.
Solve for x.
7.
Solve for x.
Linear Pair & Supplementary
Vertical Opposites
Right angle
Linear Pair & Supplementary
Vertical Opposites
Given the following information:
Solve for the value of x, y and all angles?
4x + 31 = 6x – 11 (Vertical Opposites are )
- 4x + 11 - 4x + 11
42 = 2x
2
2
x = 21
= 4(x) + 31 or = 6(x) – 11
= 4(21) + 31 = 6(21) – 11
= 115
= 115
L ? + 115 = 180 (Linear Pair Ls are supplementary)
- 115 - 115
L?
= 65
If L ? = 65 and L ? = 6y + 29
then 6y + 29 = 65
– 29 – 29
6y
= 36
6
6
y = 6
12. Given: L1 || L2; L3 || L5; L4 || L6; L1  L2 and
L 4 = 120o, and L 15 = 30o , solve all other angles
13. Solve all angles below
Itg2 U3 WS 6
1) In the picture below if BC is parallel to line EF,
(a) What is the value of x?
(b) What is the measure of angle ABC?
(c) What is the measure of angle BED?
(d) Label all the angle measurements.
L ABC = L BEF (Corresponding angles are )
3x – 12 = 2x + 12
- 2x + 12 - 2x + 12
x
=
24
L ABC = L BEF = 3(x) – 12 or = 2(x) + 12
= 3(24) – 12 or = 2(24) + 12
= 60
= 60
L BED + L BEF = 180 (Linear Pairs are supplementary)
L BED + 60 = 180
- 60
- 60
L BED
= 120
2.
Lines that look parallel are parallel, L 12 = 100o,
L 14 = 30o. Solve all angles below
3.
In the picture below if BD is parallel to line EG,
(a) What is the value of x?
(b) What is the measure of angle ACD?
(c) What is the measure of angle DCF?
(d) Label all the angle measurements.
7x – 14 = 6x + 3 (Vertical Opposites are )
- 6x + 14 - 6x + 14
x
=
17
or 4x + 7 + 6x + 3 = 180 (Corresponding & Linear Pair)
10x + 10 = 180
– 10 – 10
10x
= 170
10
10
x
= 17
or 4x + 7 + 7x – 14 = 180 (Corresponding & Linear Pair)
11x – 7 = 180
+ 7
+7
11x
= 187
11
11
x
= 17
One Example for finding all angles
L ACD = 4(x) + 7
= 4(17) + 7
= 75
L ACD + L DCF = 180 (Linear Pairs are supplementary)
75 + L DCF = 180
- 75
- 75
L DCF = 105
4. Given: : EF || GH; AB || CD; L 1 = 35o, solve all angles.
5. Given: : || are indicated; L 1 = 108o; L 8 = 22o ;
L 17 = 125o. Solve all angles below
7.
Find the measure of each labeled angle.
v
n
50 q
m
u
30
120
p r
40
6.
Given the following information:
Solve for the value of x, y and all angles?
6y + 14 = 12y – 34 (Vertical Opposites are )
- 6y + 34
- 6y + 34
48 = 6y
6
6
y = 8
6(y) + 14 or = 12(y) – 34
6(8) + 14 = 12(8) – 34
= 62
= 62
62 + L ? = 180 (Linear Pair Ls are supplementary)
- 62
- 62
L ? = 118
If L ? = 118 and L ? = 4x + 30
then 4x + 30 = 118 (Transitive Property of Equality)
– 30
– 30
4x = 88
4
4
x = 22
s
t
Use the following picture to answer the following questions
Use the following picture to answer the following questions
1) Find the measures (in degrees) of the following angles:
(a) angle AFB
(d) angle EFD
(b) angle EFB
(e) angle AFD
(c) angle AFC
1) Find the measures (in degrees) of the following angles:
(a) angle AFB
(d) angle EFD
(b) angle EFB
(e) angle AFD
(c) angle AFC
Use the following picture to answer the following questions
Use the following picture to answer the following questions
1) Find the measures (in degrees) of the following angles:
(a) angle AFB
(d) angle EFD
(b) angle EFB
(e) angle AFD
(c) angle AFC
1) Find the measures (in degrees) of the following angles:
(a) angle AFB
(d) angle EFD
(b) angle EFB
(e) angle AFD
(c) angle AFC
Use the following picture to answer the following questions
Use the following picture to answer the following questions
1) Find the measures (in degrees) of the following angles:
(a) angle AFB
(d) angle EFD
(b) angle EFB
(e) angle AFD
(c) angle AFC
1) Find the measures (in degrees) of the following angles:
(a) angle AFB
(d) angle EFD
(b) angle EFB
(e) angle AFD
(c) angle AFC
..
Perpendicular line *
Two lines are perpendicular if they
intersect to form a right angle.
Reflection
A type of translation where the image
is a mirror image flipped over the x or y
axis. The image is congruent with the
preimage.
sum of their measures is 180 degrees.
Parallel lines *
Two lines are parallel if they do not
intersect
Translations
A type of translation where the image
is moved horizontally (left or right) and
/ or vertically (up or down). The image
is congruent with the preimage,
Midpoint
A point that divides the segment into
two congruent segments.
Obtuse angle
An angle with a measure more than 90
degrees.
Congruent angles
Two angles are congruent if they have
the same measure.
Segment bisector
A segment, ray, line, or plane that
intersects a segment at its midpoint.
Transversal
A line that intersects two or more
coplanar lines at different points.
Postulate
A statement that is accepted as true
without proof
Coplanar
Points, segments, rays or planes that
are on the same plane are coplanar.
Straight angle
An angle with a measure of 180
degrees.
Vertical angles
Angle bisector
A ray that divides the angle into two
congruent angles.
Rotation
A type of translation where the image
is turned about a fixed point. The
image is congruent with the preimage.
Theorem
A statement that must be proved to be true.