Download Chapter 1 Packet 2016

Chapter 1
Essentials of
Geometry
PAP
Name: ______________________
Period: ________________
Teacher: ____________________
1st Six Weeks 2015-2016 Geometry PAP
MONDAY
Aug 24
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
25
26
27
28
1 day
Welcome
Course Syllabus
Calendar
Start Powers
Begin Vocabulary
31
1-1 Points, lines, and
planes Day 1
Give Picture
conclusions
HW: 1-1 day 1
1-1 Points, lines, and
planes Day 2
More 1-1 Points, lines
and planes
1-2 Measuring
Segments Day 1
HW: Day 2
HW: Day 2
Sept. 1
2
3
4
1-2 Measuring
Segments Day 2
1-4 Exploring Angle
Pairs
Quiz #1
1-4 Exploring Angle
Pairs
Quiz #1
HW: 1-2 Day 2
1-3 Measuring
angles
Summer Packet
Quiz
HW: 1-3
Hw: 1-4
Hw:1-4
7
8
9
10
Statements and
Conclusion Practice
Review
HW: Statements
and conclusion
practice & Review
11
Holiday
Test #1
2-5 algebraic proofs
Powers quiz
2-5 algebraic proofs
Powers quiz
2-2 Conditional
Statements
HW:
16
HW:
17
st
HW: 1-2 day 1
HW:
14
15
18
Day 1 2-6/2-7
proofs with
segments, angles,
and angle pairs
HW:
Day 2 2-6/2-7
proofs with
segments, angles,
and angle pairs
HW:
Review
Quiz #2
Review
Quiz #2
Test #2
21
22
23
24
25
3.1/3.2 Identifying
angle pairs and their
relationships
Day 2 3.1/3.2
Identifying angle
pairs and their
relationships
Holiday
Parallel line proofs
Day 1
Parallel line proofs
Day 2
HW:
HW:
HW:
HW:
28
29
30
Oct. 1
2
Review
School pics
Test #3
School pics
3.4 Find and use
slopes of lines
3.4 find and use
slopes of lines
3.4/3.5 Slopes,
writing and
graphing equations
of a line
HW:
HW:
HW:
All answer keys can be found on Mr. Schroeder’s/Ms. Zita’s Website, students are responsible for checking their work
before the next class meeting. All work must be shown and explanations given when stated in the problem, failure to do
so will result in credit not being given for the assignment.
2
3
4
Worksheet 1-1 Points, Lines, and Planes Day 1
I.
1.
Name ___________
Short Answer
Name one real-world object that suggests
a. points
b. lines
c. planes
.D
.
.
2.
Give 5 different names for this line.
3.
Two lines that have a point in common are called __________________ lines.
4.
Three points that are all on a line are _____________________ points.
5.
Four points that are not in the same plane are ____________________ points.
II.
Write each of the following using symbols.
6.
The line containing points A and B. _________
7.
A point not on AC . _________
8.
A pair of lines that intersect at point A. _________
9.
A point on AC but not on BC . _________
10.
A point between A and C. _________
E
F
.D . B
.F C
.A E. .
III.
Draw and label each figure.
11. two points, J and K
12. 3 noncollinear points: R, S, and T
13. GH
14. Line
15. plane R containing points A and B
16. CD and EF , intersecting at point Z
17.
containing points M, N, and Q
3 collinear points: C, D, and E
IV.
Determine whether each statement is true or false. If false change the statement to make
it true.
18.
Points E, J, and G are collinear
19.
Points A, F, and H are coplanar
20.
Plane ABC intersects plane AIJ in AC
21.
IJ intersects EG at point I.
22.
Points B, D, and H are coplanar.
23.
Points A, I, and C are noncollinear.
B
F
.
.
. K .A
.
E
I
.
.C
.J .G
.D
.H
5
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
6
7
1-1 Points Lines and Planes PAP Day 2
Name _____________________________
R
1) Are N, P, Q, and R coplanar?
N
Q
P
2) Are N, J, P, and Q coplanar?
M
3) Are N, M, and L coplanar?
J
L
K
4) Name in two different ways the plane that contains F, G, D, and E.
B
5) Are A, B, D, and E coplanar?
C
A
6) Are B and H collinear?
H
G
7) Are C, H, and E collinear?
D
E
F
8) Name Plane P in another way.
9) What is the intersection of ST and TR ?
S
10) What is the intersection of TR and plane P ?
T
11) What is the intersection of plane P and Plane STQ
Q
R
P
12) What is the intersection of SQ and TR ?
13) What is the intersection of plane P and plane STR?
14) What is the intersection of ST and SR ?
15) What is the intersection of plane P and SQ ?
Which of the following are collinear?
16) T and R
17) S and Q
18) S, T, and R
Which of the following are coplanar?
19) S, Q, and R
20) S, T, and R
21) S, T, R, and Q
22) ST and R
23) ST and Q
24) ST and TR
25) TR and S
26) TR and Q
27) TR and SQ
8
1-1 Mixed Practice Day 2
1) Name AB in another way.
2) Give two other names for plane Q
Q
A
3) Why is EBD not acceptable name for plane Q?
D
E
B
C
Are the following sets of points collinear?
4) AB and C
5) B and F
6) EB and A
7) F and plane Q
F
Are the following sets of points coplanar?
8) E, B, and F
9) DB and FC
10) AC and ED
11) AE and DC
12) F, A, B, and C
13) F, A, B, and D
14) plane Q and EC
15) FB and BD
Find the intersection of:
16) GK and LG
17) planes GLM and LPN
H
G
18) planes GHPN and KJP
19) planes HJN and GKL
K
L
J
M
20) KP and plane KJN
N
P
21) KM and plane GHL
22) Name plane P in another way.
23) Name plane Q in another way.
D
24) What is the intersection of planes P and Q?
25) Are A and C collinear?
26) Are D, A, B, and C coplanar?
C
B
Q
A
27) Are D and C collinear?
28) What is the intersection of AB and DC ?
P
29) Are planes P and Q coplanar?
30) Are AB and plane Q coplanar?
31) Are B and C collinear?
9
Worksheet 1-2 Measuring Segments Day 1
I.
Name___________________
Find each distance on the number line.
A B C D E F G H I J K L M N P
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
1. KN
2. PH
3. DI
4. AE  FH
5. DN  IK
6. EI  JN
II.
Find the linear distance between each pair of points with the given coordinates.
7. 15, 12
8. 19, -12
9. 7.26, - 8.7
III.
Write and solve an equation to find the length of each segment.
10. B is between A and C. AB  x, BC  2x, AC  18. Find AB and BC .
A
C
B
11. B is between E and D. BD  t  9, EB  t , ED  31. Find BD and EB
E
IV.
12.
D
B
Answer the following questions. Draw a picture.
T is between R and S. RT  2x, TS  4, RS  3x 1. Find RS and RT
R
S
T
13. A basketball coach is interested in measuring a player’s vertical jumping ability. While standing and reaching up,
the player’s hand reaches the 4-in. mark on the scale. When jumping, the player can reach the 19-in. mark. What is
the player’s vertical jumping ability?
V.
Points A, B, and C are collinear. The lengths of certain segments are given. Draw a picture and show
which point is between the other two?
13. AB  12, CB  8, AC  4.
14. BA  9, BC  12, AC  3.
VI.
15.
16.
Find the value of the variable.
AB  3x  4 , AC  40 , AB  BC
A
BC  2 x2 , AC  64 , AB  BC
A
17.
C
B
FE  2 x , EC  x2 , FC  24
F
C
B
E
C
10
18. F is between T and R. TF  3x , FR  4x  2 , TR  54 . Draw a picture and find TF and FR .
TF  _____
FR  _______
19. If PQ  QR  PR , Draw a picture and which of the points P, Q, or R is between the other two?
20. Given that R is between S and T, draw a picture and find each missing measure.
a. TS  11.75 , TR  3.4 , RS  _____
b. SR 
11
5
, RT  , ST  ______
3
3
21. Find ST if S is between R and T, and SR  2x  7 , ST  x  6 , and RT  100 .
22. If A is between B and C, AB  3x  6 and AC  2x  14 .If the length of the two segments is the same, then what is
the measurement of BC.
23.
If U is between T and B, find the value of x and the measure of TU . Draw a picture.
TU  2 x , UB  3x  1 , TB  21
24. How many different ways to name the following line with the given information. List all the ways.
A
B
C
D
25. Katy is between Houston and San Antonio. If the distance from Katy to San Antonio
is x 2  5x miles and the distance from Katy to Houston is 4x  12 miles. The total
distance from Houston to San Antonio is 120 miles . Then How far is it between each City?
11
Worksheet 1-2 Measuring Segments Day 2
22.
Name___________________
23.
12
24.
25.
26.
For the following points: (the graph is there to help, but you must show the work)
A. Find the distance between the points leaving answer in radical form.
B. Find the location of the midpoint (M) between the points.
27. A  2,3
B  4, 3
28. E 5, 3
E 1,6 
29. G  2,6 
H  4, 5 
30. J  8, 2 
K  6, 4 
Example of Radicals:
24  4 6  2 6
or
22  2 11  22
or
36  6
13
Worksheet 1-4 Measuring Angles
For the following problems find the indicated angles.
1. BD is the bisector of
m ABC = _____
A
ABC . m ABD  (2 y  3) , m DBC  ( y  12)
m DBC = _____
m ABD = _____
D
B
C
2. PD is an angle bisector of BPE . m 4  4x  12, m BPE  10x . Find m 4 .
B
D
4
P
E
3. m 2  3x, m 3  3x  9, m BPD  7 x . Find m 3 .
B
2 3
D
P
4. BD is the bisector of
m ABC = ____
 5x 
  (Hint: think proportion)
 3
ABC . m ABD  5( x  8) , m DBC  
m DBC = ____
m ABD = ____
Solve the following problems.
5.
WXY is a right angle. Z is in the interior of WXY
Is XZ the bisector of
m WXZ  (5 y  5) , m YXZ  (6 y  3) .
WXY ? Show why with work or words.
6. m ABC  130 , D is in the interior of ABC , m ABD  (3x  4) , m CBD  (4 x  14) .
Is BD the bisector of
7.
ABC ? Show why with work or words.
1and 2 are complementary. m 1  3x  5, m 2  2x . Find m 1 .
1
8. BD is the bisector of
m ABC = ____
2
ABC . m ABD  (7 x  2) , m DBC  2(46  x)
m DBC = ____
m ABD = ____
14
9. PD is an angle bisector of BPE . m 4  x  30, m BPD  3x 10 . Find m 4 .
B
D
4
P
10. m 4  72, m 2  m 3, m 2  m 3  m 4 . Find m 2 .
2 3
E
4
For problems 11-13 use the following situation. PQS with R in the interior.
11. m PQS  4x , m SQR  2x , m RQP  24 . Find m SQR and m PQS .
12. m SQR  3x  2 , m SQP  5x , m PQR  34 . Find m SQR and m PQS .
13. m PQS  6x , m PQR  3x  2 , m SQR  22 . Find m PQS and m PQR .
14. ABC is a right angle with G in the interior. If m ABG  x 2  3x and m CBG  40x , then
find the value of “x”, m ABG , and m CBG .
15. DEM with F in the interior. DEF  FEM , m DEF  x 2  2x and m FEM  10x  20 . Find
the value of “x”, and the measure of DEM .
16.
18.
17.
19.
20.
15
1-4 Exploring Angle Pairs
Directions: Draw a figure and answer the following problems.
1) 1 and 2 are supplementary angles. If m 1  (4x ) and m 2  (8x ) , then
find the measures of these angles.
2) 3 and 4 are complementary angles. If m 3  (x  24) and m 4  (x ) , then
find the measures of these angles.
3) Two lines intersect to form two vertical angles. If one vertical angle is
2x
and the other
3
is 90 , then what is the value of x?
4) Two lines intersect to form angles. If the two adjacent angles form are  4 x   and
5x
 27   , then what is the measure of those angles?
5) Two angles form a linear pair. If the angles are  4x  20   and  x   , then what
is the measure of those angles?
6) LKM is a right angle. Point X is in the interior of the angle and a ray is drawn from
K through X. If m MKX   4x  2  and m XKL   2x  20   , then find the measures
of the angles created.
7) Two angles are complementary. If one angle is  x 2  16x   and the other is  3x   , then
what is the measures of the angles?
8) m CAT is 27 . Point G is in the interior of CAT . If
m CAG   x 2   and
m GAT   6x   , then what is the value of x and the measures of the angles formed?
Find the missing values for each letter.
9)
10)
11)
f
68 j
131
d
e
13)
t
122
u
g
23
i 51
12)
67
h
14)
p
q 89
o
167
Hint #13: Remember the sum of
the angles in a triangle is ?
34
87
y
z
16
Draw a picture, find the value of the variable, and the angle measures.
15. 1 and 2 are complementary. 1  (7 x  4) , 2  (4 x  9) .
16. 1 and 2 form vertical angles. 1  (16 x  9) , 2  (4 x  3) .
17. 1 and 2 are supplementary. 1  (4 x  5) , 2  ( x) .
18. 1 and 2 are complementary. 1  (8x  6) , 2  (14 x  8) .
19. 1 and 2 form vertical angles. 1  (5x) , 2  ( x  16) .
20. 1 and 2 form a linear pair. 1  (7 x  10) , 2  (3x) .
21. 1 and 2 form a right angle. 1  (4 x  3) , 2  ( x  8) .
22. An angle is 40 more than its complement. What is the measure of that angle?
23. The measure of one angle is three times its complement. Find the measure
of the angles.
24. The measure of the supplement of an angle is 30 more than twice the measure
of the angle. Find the measure of the angles.
25. An angle is 65 less than its supplement. What is the measure of that angle?
26. The measure of an angle is eight times the measure of its supplement, what
is the measure of that angle?
27. The difference in the measures of two supplementary angles is 38. Find the
measures of the angles.
28.
31.
29.
32.
30.
33.
17
Statement and Conclusion Practice
Name _________________________
1) If D is between A and C , then _____________________________________________
2) If the sum of 4 and 7 is 90, then _________________________________________
3) If angle AFB and BFR are adjacent, then _________________________________
4) If 3 and 9 are a linear pair, then ________________________________________
5) If GH bisects JY at point T , then ___________________________________________
6) If RTI  ITP , then _______________________________________________________
7) If 5 and 8 have a sum of 180, then ______________________________________
8) If G is in the interior of HIP , then _________________________________________
9) If O is between points D and G , and DO  OG , then ___________________________
10) If TGF and FGP form a linear pair, then _________________________________
11) If 4 and 6 are vertical, then ____________________________________________
Use the pictures to make a valid conclusion.
Picture
Conclusion
A
12)
C
B
D
13)
A
B
C
14)
J
K
H
15)
I
L
N
38
P
52
M
R
Q
18
Picture
16)
Conclusion
S
U
T
V
17)
W
X
Y
Z
18)
E
F
G
19)
F
G
D
56
124
E
I
H
20)
3
2
21)
J
K
L
M
N
22)
P
Q
R
19
Worksheet on Chapter 1
Use your own paper.
D
H
1.Name points collinear with pt. F.
2.Name points coplanar with pt. G.
3.Give another name for AF .
4.Name a point between B and D.
5.Name a point noncoplanar to pt. F.
6.Name a point noncollinear but coplanar to pt. F and pt. C.
7.Name a line that is not in plane K.
E
A
F
C
G
K
H
B
Find the distance between each pair of points and the midpoint. Simplify all radicals.
8.
A(4, 5); B(–4, 7)
9.
C(–1, –1); D(4, 1)
10.
E(0, 9); F(7, 3)
11.
G(0, 1), H(1, 0)
Write and solve an equation to find the length of each segment.
12.B is between A and C. AB = y – 2, BC = 2y, AC = 22. Find AB and BC.
13.B is between E and D. EB = x, BD = 30, ED = 4x + 6. Find EB and ED.
14.T is between R and S. RT = 2x, TS = 4, RS = 3x – 1. Find RT and RS.
15.B is between A and C. AB = 3x + 4, AC = 50, AB  BC . Find AB and BC.
16.J is between R and P. JR = x2, JP = 4x, RP = 32. Find JR and JP.
17.J, K, L are collinear with coordinates j, k, l. If j = –5, k = 14, and KL = 25. Give two possible answers for JK and JL.
2
18.P is between M and N. PM = PN, MN = 98. Find PM and PN.
3
Determine whether each statement is always, sometimes, or never true. Give a reason for your answer.
19.mABC + mCBD = mABD.
20. RS and RT are the same ray.
21.ABC and CAB are the same angle.
22.If E is between D and F, then ED and EF make up DF .
Write and solve an equation to find the measure of each angle.
23.R is in the interior of PQS. mPQS = 80°, mRQP = 37°. Find mSQR.
24.R is in the interior of PQS. mSQR = 3x – 2, mSQP = 5x, mPQR = 34°. Find mSQR and mSQP.
25.If PC is the bisector of DPB and mCPD = 28°, then mBPC =
26.If PC is the bisector of DPB and mDPB = 62°, then mDPC =
Be able to define:
acute angle
adjacent angles
angle
angle bisector
collinear
congruent angles
congruent segments
distance between points
interior of an angle
line segment
measure of an angle
midpoint
ray
right angle
segment
straight angle
opposite rays
perpendicular
obtuse angle
Know the following:
undefined terms
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
20
Review Chapter 1 PAP
Determine whether each statement is true or false. If false explain why.
1 Points B, A, and H are collinear
B
2. Points A, F, and H are coplanar
.
3. Plane ABC intersects plane AIJ in AC
4. IJ intersects EG at point I.
F
.
. K .A
.
5. Points B, C, D, J are noncoplanar.
E
I
.
.C
.J .G
.D
.H
6. Points A, I, and C are noncollinear.
7. Planes BCD, plane DHE, and plane BFE intersect at E.
Refer to the number line below to answers questions 8-14
8. AB
9. DA
10. FB
11. CF
12. AC
13. What is the coordinate of the midpoint of CF ?
14. What segment is congruent to DE ?
15. If R is between Q and T, QR  14 , and RT  5 , then what is QT ?
16. What is the midpoint of a segment with coordinates D  6,6  and E  2,2 ?
17. If A  B , mA  4x  7 , and mB  3x  3 , find mA ?
18. Find m1 .
19. ST is the bisector of
 5x 
.
 3
RSU . m RST  5( x  8) , m TSU  
Find mRSU .
21
20. Point E is between F and C. Use the given information to write an equation. Solve the
equation, then find FE and EC. FE  2 x , EC  x2 , FC  24
21. M is the midpoint of AB . Find AB. AM  2 y  6 , MB 
5y
2
Find the midpoint of the following order pairs.
22.
23.
Find the distance between the following points. Leave answer as a radical.
24. A  2,3
B  4, 3
25. E 5, 3
F  2,3
26. Give the endpoint (5, 4) and the midpoint (1, 5) , find the other endpoint.
27. Give the endpoint (2, 6) and the midpoint (1,8) , find the other endpoint.
28. Find x and y.
Are the following polygons convex or concave.
29.
30.
Determine if the polygon is regular, equilateral, or equiangular. Also name the figure by the number of sides.
31.
32.
33.
22
34. The figure is a regular polygon. Find the value of x.
Draw the following figures.
35. A quadrilateral that is equiangular
36. A regular pentagon
37. m ABC  130 , D is in the interior of ABC , m ABD  (3x  4) , m CBD  (4 x  14) .
Is BD the bisector of
ABC ? Show why with work or words.
38. B is between A and C, BC  2 x2 , AC  64 , AB  BC . Find x.
39. 1 and 2 are supplementary angles. If m 1  (4x ) and m 1  (8x ) , then
find the measures of these angles.
40. 3 and 4 are complementary angles. If m 3  (x  24) and m 4  (x ) , then
find the measures of these angles.
41. Two angles form a linear pair. If the angles are  4x  20   and  x   , then what
is the measure of those angles?
42. LKM is a right angle. Point X is in the interior of the angle and a ray is drawn from
K through X. If m MKX   4x  2  and m XKL   2x  20   , then find the measures
of the angles created.
43. Two angles are complementary. If one angle is  x 2  16x   and the other is  3x   , then
what is the measures of the angles?
44. m CAT is 27 . Point G is in the interior of CAT . If m CAG   x 2   and
m GAT   6x   , then what is the value of x and the measures of the angles formed?
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Chapter 1 Overview
1) How many undefined terms are there for Geometry? 3
2) What are the undefined terms of Geometry? Point, Line, Plane
3) Define point, draw a sketch of a point, and what is the label for a point? A place in space, it has not dimensions.
It is represented by a dot. Label: A, B, C
B
C
A
4) Define line, draw a sketch of a line, and what is the label for a line? It extend without end in two directions. It
has one dimension, length. Label: AB or line
B
A
5) Define plane, draw a sketch of a plane, and what is the label for a plane? It extends without end, it has 2
dimensions, it is represented by a shape that looks like a floor or wall. Even though it appears to have edges,
it does not. Label: ABC or plane 
B
C
 A
6) What are collinear points? Give a sketch of collinear points. Points on the same line.
C B
A
7) What do you do to determine if points are collinear for a equation of a line? You plug the points end and if the
statement is true, then the point in collinear.
8) What are coplanar points? Give a sketch of coplanar points. Point on the same plane.
B
C
A
9) What are defined terms? Terms that can be described using known words.
10) Define line segment, draw a sketch of a line segment, and what is the label for a line segment? Part of a line
that consists of two points, called endpoints, and all points on the line that are between the endpoints. Label:
B
AB
A
11) Define ray, draw a sketch of a ray, and what is the label for a ray? Part of a line that consists of a point called
an endpoint and all points on the line that extend in one direction. Label: BA
B
A
12) What are opposite rays? Draw a picture of a pair of opposite rays and a pair that are not opposite rays. Two
rays that share an endpoint, and extend in opposite directions.
A
B
Opposite Rays
C
A
B
C
Not Opposite Rays
13) What is an intersection? Set of points that two or more geometric figures have in common.
14) Draw an intersection of the following: 2 lines, 2 planes, a line and a plane. A point, a line, a point or all the
points on the line if the line is in the plane.
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15) What is a postulate(axiom)? A rule that is accepted without proof.
16) What is the Ruler Postulate? See Postulate sheet. Distance between two points is the absolute value of the
difference.
17) How do you find distance on a number line? Absolute value of the difference
18) Give an example of between, and an example of not between.
A
B
B
A
between
Not
between
C
C
19) What is the segment addition postulate? Draw a picture for your definition. If B is between A and C then
AB+BC=AC.
B
A
C
20) What is the algebraic set-up for the segment addition postulate? Part + Part = Whole
21) What are congruent segments? What is the algebraic set-up for congruent segments? 2 segments that have
the same length. Segment = Segment
22) Define midpoint. Draw a picture of midpoint. A point that creates 2 congruent segments.
B
A
C
23) What is the algebraic set-up for midpoint? Segment = Segment
24) How do you know if a point is a midpoint? What marks can help determine this? The congruence marks on the
segment. Tick marks.
25) Define segment bisector. Draw a picture of a segment bisector. A point, ray, line, segment, or plane that
intersects the midpoint.
B
A
C
26) How many different geometric things can be a bisector? list them. 5, point, line, plane, segment, and ray.
27) What is the difference between a midpoint and a segment bisector? Midpoint creates 2 congruent segments,
bisector just finds the midpoint.
 x1  x2 y1  y2 
,
 or average of the x and y values.
2 
 2
28) What is the midpoint formula? M 
29) What is the distance formula? d 
 x2  x1    y2  y1 
2
2
30) What is an easier way to do distance between 2 points? Using Pythagorean Theorem, A2  B2  C 2
31) What is an angle? 2 rays that have a common endpoint. Measured in angular degreees
32) Draw an angle and list all the parts of an angle.
vertex
exterior
sides interior
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33) How do you name an angle? 3 points on the angle with the middle letter being the vertex, or list it by number
if one is located in the interior by the vertex.
34) How many different ways are their to name an angle? Three
35) What is one way not to name an angle and why? By only the vertex, because multiple angles may have the
same vertex, which means your answer would be too vague.
36) What is the protractor postulate? See postulate sheet, measure of an angle is the absolute value of the
difference in their positions on a protractor.
37) What are the 4 ways an angle can be classified and what does each one mean? Acute 0<x<90, Right x=90,
Obtuse 90<x<180, Straight x=180 x = the angle measure
38) What is the angle addition postulate? Draw a picture for your definition. If P is in the interior of RST , then
mRSP  mPST  mRST .
R
P
S
T
39) What is the algebraic set-up for angle addition postulate? Part + Part = Whole
40) What are congruent angles? How are they marked in a diagram? Draw a picture. Angles that have the same
measure. Arcs mark congruent angles.
41) What is the algebraic set-up for congruent angles? Angle = Angle
42) What is the difference between “congruent” and “equal to”? Congruent means same shape, while equal to is
for actual numbers and lengths.
43) Define angle bisector and draw a picture. A ray that divides an angle in to two congruent angles.
Angle bisector
44) What is the difference between an angle bisector and a segment bisector? An angle bisector actually creates
two congruent angles, but a segment bisector only show where the midpoint is. Also the difference is angles
and segments.
45) Define complementary angles and draw a picture. Two angles whose sum is 90 degrees.
46) What is the algebraic set-up for complementary angles? Angle + Angle = 90
47) Define supplementary angles and draw a picture. Two angles whose sum is 180 degrees
48) What is the algebraic set-up for supplementary angles? Angle + Angle = 180
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49) Define adjacent angles and draw a picture. Two angles that share a common endpoint and ray.
50) What is the algebraic set-up for adjacent angles? There is not set up, adjacent angles tell nothing of their
measures.
51) Do complementary and supplementary angles have to be adjacent? Why? No, because it only says that their
sums must be 90 or 180, so they do not have to be adjacent.
52) Define linear pair and draw a picture. Two adjacent angles whose noncommon sides are opposite rays.
53) What is the algebraic set-up for linear pair of angles? Angle + Angle = 180
54) What is the difference between linear pair and supplementary angles? Linear pair must be adjacent, but
supplementary do not.
55) Define and draw a picture of vertical angles. Two angles formed by 2 pairs of opposite rays.
56) What can be determined by a diagram? Only things that are define, like collinear, coplanar, interior, exterior
or other definitions.
57) What can not be determined by a diagram? Measures and congruent.
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