Period ____
Name _________________________________________
GP
UNIT 3 – POINTS, LINES, PLANES, AND ANGLES
Be able to Define, identify or illustrate the following terms
Angle
Vertex
Interior of an angle
Exterior of an angle
Measure
Degree
Acute angle
Right angle
Obtuse angle
Straight angle
Congruent angles
Angle bisector
Adjacent angles
Linear pair
Complementary
angles
Supplementary angles
Plane
Vertical angles
Ray
Collinear
Noncollinear
Coplanar
Bisector
Endpoint
Midpoint
Congruent
Euclidean
Point
Non-Euclidean
Line
Dates, assignments, and quizzes subject to change without advance notice.
Monday
24
Tuesday
25
Practice
Quiz with Proofs
1
Review
TEST 3 – PART 1
Angle Vocab
AAP and Bisectors
Block Day
19/20
Notations and
Segments
Segment Addition and
Bisector Segments
26/27
Angles with Advanced
Algebra
Angle Pairs
Friday
21
Segment Constructions
and
Segments with
Advanced Algebra
28
Angle Constructions
Mixed Practice
2
TEST 3 - PART - 2
Wednesday or Thursday, 9/19 – 20/12
Points, Lines, and Planes & Segment Addition/Bisector
I can understand the differences between Euclidean and Non-Euclidean Geometry.
I can identify, name, and draw points, lines and planes.
I can justify relationships between points, lines and planes using postulates and theorems.
I can solve problems using Segment Addition Postulate.
I can solve problems using segment bisectors/midpoint.
PRACTICE: p 9 (13-19, 25-29, 31-34) and p 17 (15, 17-18, 24-26, 32-33 Justify #15, 18, 32,33) (24 problems)
Friday, 9/21/12
Segment Addition and Segment Bisector
I can recognize the markings used in geometric constructions of segments.
I can solve problems using Segment Addition Postulate with advanced algebra.
I can solve problems using segment bisectors/midpoint with advanced algebra.
PRACTICE: p 17 (#5 copy and bisect the given segment) & Segments with Advanced Algebra Worksheet
Monday, 9/24/12
QUIZ: Segment Addition and Segment Bisector
PRACTICE: Complete Block Day and Friday’s Assignments
Tuesday, 9/25/12
Angle Addition and Angle Bisector
I can use proper notation and symbolism for angles.
I can solve problems using Angle Addition Postulate.
I can solve problems using angle bisectors.
PRACTICE: pg. 25 (#17-18, 29-32, 38, 41-42, 44-45, Justify 17, 18, 29, and 31) (11 problems)
Wednesday or Thursday, 9/26 – 27/12
Angle Addition and Angle Bisector
I can solve angle problems using advanced algebra
I can solve problems using complementary and supplementary angles.
I can solve problems using linear pairs and vertical angles.
PRACTICE: Angles with Advanced Algebra & Angle Relationships Worksheets (assigned problems only)
Friday, 9/28/12
Mixed Practice
I can recognize the markings used in geometric constructions of angles.
I can solve problems using Segment Addition/Bisectors.
I can solve problems using Angle Addition/Bisectors.
PRACTICE: Mixed Practice Worksheet
Monday, 10/1/12
Review
Test 3: Part 1
PRACTICE: Review Assignment
Tuesday, 10/2/12
Test 3: Part 2
Score:
Segments Vocabulary
Name:
Per:
We will use many notations and symbols this year in Geometry. You may know many of them already. Listed
below are some frequently used symbols. Try to translate each symbol into the word or phrase that it represents.
Symbol or Word
P
XY
l
S
ABC
RS
AB
GH
First Guess of Meaning
Correct Meaning
Picture & Notes
Symbol or Word
≅
Coplanar
Endpoint
Collinear
Noncollinear
Bisect
Midpoint
Intersection
Congruent
segments
First Guess of Meaning
Correct Meaning
Picture & Notes
Segments with Advanced Algebra Worksheet
1. Find DK if D is between I and K and DI =
2
7
2
x + 5 , IK = x + 4 ,and DK = x + 2
3
3
3
2. SW = 2x + y, WC = x – 2y, W is the midpoint of SC, and SC = 20, find the values of x and y.
3. CT = x2, CA = 3x – 4, and AT = 4x – 8, find the value(s) of x if A is between C and T.
4. I is between W and N. Find the value(s) of x and the length of IN if WI = x 2 + 2 x , IN = x 2 − 5 ,
and WN = 3 x 2 − 3 x − 11 .
5. S is the midpoint of TU . If TS = 2 x − 11 and TU = x 2 − 4 x − 31 ,find SU.
6. Find the value(s) of r if LE = r 2 − 2r − 6 , EG = 3r + 10 , LG = 2r 2 − 6r + 16 , and E is between LG
7. Given the following information, draw a diagram and answer the following questions.
Given: U is between L and N and C is between N and H; LU = CH; UH = 25; NH = 12; NC = 7.
Find: LH =
; UN =
8 – 10: Use the given line segment to find the value(s) of x, RA, AT, RT..
R
A
8. RA = 4x – 25, AT = 11x – 25, and RT = x2.
x = __________; RA = ________
AT = _________; RT = ________
9. RA = x 2 − 3 , AT = 4 x + 1 , and RT = 2 x 2 + 2 .
x = __________; RA = ________
AT = _________; RT = ________
10. RA = x 2 − 2 x − 2 , AT = 2 x 2 + 3 x − 24 , and RT = x 2 + 5 x − 10
x = __________; RA = ________
AT = _________; RT = ________
T
Name _________________________________________
GL
Period ____
Notes - Naming Angles
9/12 – 9/26/08
GP
Examples: Name all angles in the picture in all possible ways.
I
J
C
A
B
C
H
E
D
For questions # 1 – 4 name all angles in the picture in all possible ways. Classify the angles as acute,
obtuse, right, or straight.
B
1.
F
2.
A
1
D
2
1
E
A
G
3.
4.
H
I
O
4
3
J
G
D
E
A
2
U
Angles with Advanced Algebra
For questions 1-4, solve for x. Be sure to check for extraneous solutions.
1)
2)
(10 x + 5)°
A
P
A
( x 2 + 12 x )°
P
( x 2 − 5 x )°
(2 x + 24)°
T
(7 x + 20)°
T
S
S
3)
( x 2 )°
4)
(9 x − 42)°
P
2
A
P
A
( x − 6 x )°
(24 x + 50)°
(4 x − 14)°
T
T
S
S
5) F is in the interior of NAL . If mNAF = x 2 − 7 x + 1 , mFAL = x 2 − 6 x − 13 ,and
mNAL = 3 x 2 − 5 x + 4 . Find the value of x and mNAL .
6) KH bisects JKL . If mJKH = 6 x + 3 and mHKL = 8 x − 7 , find mJKL .
7) D is in the interior of ABC . Solve for x if mABD = ( x 2 − 2 x)° , mDBC = (4 x + 1)° , and
mABC = (6 x − 2)° . Are either of your solutions extraneous?
8) If YU is the angle bisector of MYD , mMYD = x 2 + 6 x − 4 , and mMYU = x 2 − 2 x + 10 ,
find mUYD .
9) M is in the interior of JKL . If mJKL = (2 x 2 + 3 x)° , mJKM = (3 x 2 − 24)° , and
mMKL = (3 x − 12)° , find mMKL .
10) YW bisects XYZ . Solve for t if mXYZ = (t 2 − 8)° and mXYW = (3t + 4)° .
For #11 and #12, tell whether BD bisects ABC , and explain how you know.
11) Is BD an angle bisector?
How do you know?
12) Is BD an angle bisector?
(50 + 2x)°
A
(–10x + 3)°
How do you know?
(6x + 15)°
A
(4x + 4)°
D
(–x + 21 )°
B
D
(10x – 1)°
C
B
C
Angles Relationships: Notes and Practice
Linear Pair Theorem:
Vertical Angle Theorem:
Supplementary Angles:
Complementary Angles:
1. Which set of angles form a linear pair?
1
2
4
2. Which set of angles form vertical angles?
1. x =______
2. y =_______
y°
3
3. a =_____
150°
4a° 120°
x°
4. w =_____
63°
105° (w – 10)°
5. t = _______
7t°
6. x =_____
(3t + 20)°
mMAT =_______
M
(7x – 14)°
T
(2x + 5)° H
A
7. x =________
mPIR =_______
mRIM =_______
P
(4x + 24)°
8. p =______
mBNK =______
B
(7p + 15)°
(5p – 3)°
S
N
I
(7x + 3)°
A
R
M
K
9. x = ______
10. x = ______
2x°
(7 x + 53)°
(3x + 85)°
( x + 39)°
11. x = ______
12. x = ______
(100 + 30 x)°
30x°
−60x°
(70 + 5 x)°
13. An angle is 70° smaller than its supplement. Find the two angles.
14. An angle exceeds its complement by 2°. Find the angle.
15. Find an angle that is twice its complement.
16. An angle is 33° less than one-half its supplement. Find the angle.
17. Find an angle that is 30° less than twice its supplement.
18. What is the supplement of the complement of 53°?
19. Write and simplify an expression for the supplement of B , if mB = (5n + 6)° .
Angles Relationships with Advanced Algebra
Use the diagram below for questions 8 and 9
1. UC is the angle bisector of NUH and
mLUH = 31w + 15 . Find mNUH .
N
C
9w + 3
14w − 9
8. Find mTAS if
TAS = 7 w + 10 ,
KAS = 3w + 18 , and
TAK = w2 + 8w − 20
S
A
H
U
L
T
9. Find the value(s) of x if
TAS = x 2 + 2 x + 1 , TAK = 2 x 2 − 3 x + 37 ,
Use the diagram below for questions 3 and 4:
and AS bisects TAK .
W
For 10-14, find the values of x and y and each angle
measure.
T
3
X
2
1
Y
10.
Z
(15 y − 7x)°
(3 y − 2 x)°
2. If YT bisects WYZ and mXYW is four
times as large as m1 , what is the measure
of 3 ?
( x + 9 y)°
3. In the diagram above,
if 1 ≅ 2 , m1 = 3 x + y , and
m 2 = y + 90 , find x.
11.
( x + 3 y)°
( y + 110)° ( x − 4 y)°
Use the diagram below for questions 4 and 5:
1
4
2
3
12.
( x + 25)°
4. Solve for x if 1 = x 2 and 3 = 3 x + 10
( y − 4 x )°
( y − 44)°
5. Solve for y if 2 = y 2 + 50 and 3 = 146 − 8 y
Use the diagram below for questions 6 and 7:
13.
6. Find the value(s) of x
in the given diagram if
SAN = x 2 ,
DAN = 5 x + 17 ,
and SAD = 3 x + 20
( x − 7 y )°
S
N
(8 x + 7)°
(5 x − 3 y + 90)°
A
D
7. In the diagram above: If AN bisects SAD ,
SAN = 2 x − 3 y , DAN = x + y ,and
mSAD = 50° , find the value of x and y.
14.
(12 x + 10)°
(2 y + 10)°
(7 x + 35)°
K
Mixed Practice Worksheet
2
2
1. RA = x − 3 , AT = 4 x + 1 , and RT = 2 x + 2 .
R
A
T
x = __________; RA = ________
AT = _________; RT = ________
2
2
2
2. RA = x − 2 x − 2 , AT = 2 x + 3 x − 24 , and RT = x + 5 x − 10
x = __________; RA = ________
AT = _________; RT = ________
Proof 2:
Given: K is between I and E
IE = 14 x − 7
Proof 1:
Given: A is the midpoint of CT .
3x + 4
5x − 8
A
C
2(3x − 1)
T
I
1.
Reason
Statements
2.
2.
4.
3.
4.
5.
5.
6.
E
Fill in the table with your proof (Note: You may not
use all rows.)
1.
3.
K
Solve for x.
Solve for x. (Complete the proof)
Statements
5x
6.
7.
8.
9.
Reason
2
3. D is in the interior of ABC . Solve for x if mABD = ( x − 2 x)° , mDBC = (4 x + 1)° , and
mABC = (6 x − 2)° . Are either of your solutions extraneous?
4. x = ______; y = ______;
mNAE = ______; mRAN = ______
L (36x–9y)° E
A
(10x–12y)°
(12x+18)°
N
R
Proof 3:
Proof 4:
x =________ ; mABC = _________
(16x-2)°
QS bisects PQR . mPQS =(5x+13)° ;
mPQR =(15x - 6)°. Find x and mSQR .
Fill in the table with your proof (Note: You may not
use all rows.)
A (9x-7)°
D
(3x+17)°
B
C
Solve for x. (Complete the proof)
Statements
1.
2.
Statements
Reason
1.
2.
3.
4.
3.
4.
5.
6.
7.
5.
8.
6.
9.
Reason