Geometry Unit 4 Homework Packet Name Unit 4 Homework 1 Unit 04.pdf · Geometry Unit 4 Homework...
Transcript of Geometry Unit 4 Homework Packet Name Unit 4 Homework 1 Unit 04.pdf · Geometry Unit 4 Homework...
Geometry Unit 4 Homework Packet Name______________________________
Unit 4 Homework 1 Use your notes to help you complete the following algebraic “proofs”.
#1 – 2: Use the list at the right to fill in the blanks below. In a few
days we’ll have similar but different reasons to use.
1. If 5x – 8 = –42, prove x = –6.8 Statements Reasons
1. 5x – 8 = –42 1. Given
2. 5x – 8 + 8 = -42 + 8 2.___________________________________ 5x = -34
3. (1/5)5x = (1/5)-34 3. ___________________________________
4. x = -6.8 4. ___________________________________
2. If 2x + 3 = -½x + 1, prove x = –4/5
Statements Reasons
1. 2x + 3 = -½x + 1 1. Given
2. 2x + ½x + 3 = -½x + ½x + 1 2. ______________________________________ 2.5x + 3 = 1
3. 2.5x + 3 – 3 = 1 – 3 3. ______________________________________ 2.5x = -2
4. 2.5x/2.5 = -2/2.5 4. _____________________________________ x = -0.8 x = -4/5
3. If 2(x – 4) + 4(2 – x) = 5x – 4(x + 1), prove x = 4/3 Statements Reasons
1. ________________________________________ 1. ______________________________________
2. 2x – 8 + 8 – 4x = 5x – 4x – 4 2. ______________________________________ –2x = x – 4
3. –2x – x = x – x – 4 3. ______________________________________ –3x = –4
4. –3x/–3 = –4/–3 4. _____________________________________ x = 4/3
Basic Mathematical Properties Distributive Property
Commutative Property Associative Property
Additive Identity Multiplicative Identity
Additive Inverse Multiplicative Inverse
Geometry Unit 4 Homework Packet Name______________________________
#4 – 13: Are the congruent and equal signs used correctly for the geometric notation? Circle the correct uses.
4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Geometry Unit 4 Homework Packet Name______________________________
Unit 4 Homework 3
#1 – 5: Name the property that justifies the statement.
_____________________1.
_____________________2. If RST XYZ, then XYZ RST.
_____________________3. If AB = CD and CD = EF, then AB = EF.
_____________________4. If , then .
_____________________5. mRST = mRST
#6 – 9: Use your notes to complete the following proofs.
6. Given: CD = 2 in.
XY = 2 in.
Prove: CD = XY
7. Given: WZ = XY
ZY = WX
WZ = ZY
Prove: XY = WX
8. Given: MT = ½RT
RM = MT
Prove: RM = ½RT
Statements Reasons Statements Reasons
Statements Reasons
R
M
T
S
C D
X Y
W X
Y Z
Geometry Name______________________________
9. Given: C is the midpoint of
CD = ½BD
Prove: BC = ½BD
#10 – 15: Is the geometric notation used below correctly? Write ‘yes’ if they are correct and ‘no’ if they are not. ________10. ________11. ________12. ________13. ________14. ________15.
Statements Reasons
1.C is the midpoint of 𝐷𝐵 1.
2. 𝐵𝐶 𝐶𝐷 2.
3. BC = CD 3. Definition of
4. CD = ½BD 4. Given
5. BC = ½BD 5.
B
C
D
A
Geometry Name______________________________
Unit 4 Homework 4 #1 – 6: Name the property/definition that justifies the statement.
_____________________1. If AB CD and CD ST , then AB ST .
_____________________2. mABC = mABC
_____________________3. If XYZ RST and ABC RST, then XYZ ABC.
_____________________4. If XY = YZ, then YZ = XY.
_____________________5. If AB CD , then AB = CD.
_____________________6. If BC CD , then C is the midpoint of .
#7 – 11: Complete the following proofs.
7. Given: AD + DE = AE
AD = EB
Prove: EB + DE = AE
8. Given: ma + mb = 180
ma = mc
Prove: mc + mb = 180
9. Given: m1 + m2 = 180
m3 + m2 = 180
Prove: m1 + m2 = m3 + m2
Statements Reasons
Statements Reasons
C
A D E B
a b
c
Statements Reasons
Geometry Name______________________________
10. Given: ,
Prove:
11. Given:
Prove:
E
B
D
C
A
1 2
Statement Reasons
1. 𝐴𝐶 𝐵𝐷 𝑎𝑡 𝐸 1.
2. <BEC is a right angle 2.
3. 3. If an angle is a right angle, then its measure is 90 degrees.
4. 4. Given
5. 5. Substitution Postulate
Statement Reasons
1. 𝐴𝐶 1.
2. 2. The sum of parts equals the whole.
3. 𝐴𝐵 𝑥 3. Given 𝐵𝐶 𝑥
4. 4.
5. 𝑥 𝑥 5. Distributive Property
6. 6x = 30 6. Subtraction Property
7. x = 5 7. Division Property
Geometry Name______________________________
Unit 4 Homework 5 Complete the following proofs.
1. Given: PQ = SR 2. Given:
Prove: PR = QS Prove:
3. Given: 4. Given: mPQR = mTQS
Prove: Prove: mPQS = mTQR
5. Given: m1 = m2
m3 = m4
Prove: QPS QRS
Statements Reasons
1. PQ = SR 1.
2. QR = QR 2.
3. PQ+QR = SR+QR 3.
PR = SQ
P Q R S
A
C
P
D
B
Statements Reasons
1. 𝐴𝑃 𝐶𝑃 1.
𝐵𝑃 𝑃𝐷
2. 𝐴𝑃 𝐵𝑃 𝐶𝑃 𝑃𝐷 2.
𝐴𝐵 𝐶𝐷
Statements Reasons
1. 𝑃𝑄 𝑅𝑆 1. Given
𝑄𝑆 𝑆𝑇
2. 2.
𝑃𝑆 𝑅𝑇
R S
Q
T
P
R
P
Q S
T
Statements Reasons
1. mPQR = mTQS 1. Given
2. mRQS = mRQS 2.
3. mPQR + mRQS = 3.
mTQS + mRQS
mPQS = mTQR
Statements Reasons
1. m1 = m2 1. Given
m3 = m4
2. m1 + m3 = m2 + m4 2. Addition Post. (1)
mQPS = mQRS
3. QPS QRS 3.
S R
P Q 1
2 4
3
Geometry Name______________________________
Complete the following proofs.
6. Given:
Prove:
Explain (in words) how/why the use of the Addition Postulate in the proof below is incorrect.
7. Given:
Prove:
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
P
B
l
C
A
Statement Reasons
1. 𝐿𝑖𝑛𝑒 𝑙 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 𝐴𝐵 𝑎𝑡 𝑃 1.
2. 2. A segment bisector intersects a segment at its midpoint
3. 𝐴𝑃 𝑃𝐵 3.
4. 4. Definition of congruence
5. 5. Given
6. 6.
A
C
P
D
B
Statements Reasons
1. 𝐴𝑃 𝐶𝑃 1.
𝐵𝑃 𝐷𝑃
2. 𝐴𝑃 𝑃𝐷 𝐶𝑃 𝐵𝑃 2. Addition Postulate
𝐴𝐵 𝐶𝐷
Geometry Name______________________________
Unit 4 Homework 6 Complete the following proofs.
1. Given: LM = PN
XM = XN
Prove: LX = PX
2. Given:
Prove: PQ = SR
3. Given: Prove:
4. Given:
C is the midpoint of
D is the midpoint of
Prove:
Statements Reasons
1. LM = PN 1. Given
XM = XN
2. LM–XM = PN–XN 2.
LX = PX
Statements Reasons
1. 𝑃𝑅 𝑆𝑄 1. Given
2. 2. Reflexive Postulate
3 3.
4. PQ = SR 4.
Statements Reasons
1. 𝑚 𝐴𝐵𝐶 𝑚 𝐷𝐶𝐵 1. Given
𝑚 𝑎 𝑚 𝑏
2. 2.
L
N
X
M
P
P Q R S
Statements Reasons
1. C is the midpoint of 𝐵𝐷 1. Given
D is the midpoint of 𝐶𝐸
2. 𝐵𝐶 𝐷𝐶 2.
𝐶𝐷 𝐸𝐷
3. 𝐵𝐶 𝐸𝐷 3.
4. 𝐶𝐷 𝐶𝐷 4.
5. 5. Addition Postulate
Geometry Name______________________________
5. Given: AB = BC
Prove: 2BC = AC
6. Complete the flow chart proof:
Given:
Prove:
7.
Given:
Explain why is not the bisector of in the picture to the left.
____________________________
____________________________
____________________________
Statements Reasons
1. AB = BC 1. Given
2. 2. The sum of the parts = whole.
3. 3.
A B C
Geometry Name______________________________
Unit 4 Homework 7 Complete the following proofs.
1. Given: AF = BE
AD = 2AF
BC = 2BE
Prove: AD = BC
2. Given: AD = AB
Prove:
3. Given:
Prove:
D
F
A
C
E
B
Statements Reasons
1. AF = BE 1. Given
2. 2. Multiplication Postulate
3. AD = 2AF 3.
BC = 2BE
4. 4. Substitution Postulate
Statements Reasons
1. 1. Given
2. 𝐴𝐷
𝐴𝐵
2.
3. 3. Given
4. 4.
5. 𝐴𝐸 𝐴𝐹 5.
Statements Reasons
1. 1. Given
2. 2.
3. 3.
A
C
B
D
Geometry Name______________________________
4. Given: AD = BC AE = CF
Prove:
5. Given:
Prove:
6. Given: mz = mw mx = my Prove:
7. In parts a – c, circle whether each proof would use the addition postulate or subtraction postulate.
a) Given: XWZXYZ
ZWYXYW
Prove: YWXWYZ
Addition Postulate or Subtraction Postulate
b) Given: ZWYXYW
YWXWYZ
Prove: XWZXYZ
Addition Postulate or Subtraction Postulate
c) Given: YZXWXZ
ZXYXZW
Prove: YZWWXY
Addition Postulate or Subtraction Postulate
Statements Reasons
1. 1. Given
2. 2. Subtraction Postulate
3. 3.
Statements Reasons
1. 1. Given
2. 2.
D
E
A
C
F
B
Z S Y
W R X
1
2
3 4
Statements Reasons
1. 1. Given
2. 2.
3. 3.
W X
Y Z
Geometry Name______________________________
Unit 4 Homework 8 1. Given:
Prove:
2. Given:
Prove:
3. Given: bisects CDA
3 1 4 2 Prove: 3 4
4. Given:
D is the midpoint of
E is the midpoint of
Prove:
Statements Reasons
1. 1. Given
2. 2.
3. 3. Given
4. 4.
D
E
A
C
F
B
Statements Reasons
1. 1. Given
2. 2.
3. 3.
A
B
C
D E
Statements Reasons 1. D is the midpoint of 𝐴𝐵 1. Given E is the midpoint of 𝐶𝐵
2. 𝐴𝐷 ½𝐴𝐵 2.
𝐶𝐸 ½𝐶𝐵
3. 𝐴𝐵 𝐶𝐵 3.Given
4. 4.
Geometry Unit 4 Homework Packet Name______________________________
5. Given:
A is the midpoint of
D is the midpoint of
Prove:
6. Given:
Prove: a)
b) D is the mdpt of
7. A student was given the proof shown below.
Given: Prove:
Statements Reasons
1.
1. Given
2. 2. (Addition Postulate)
3. 3. Given
4. 4.
5. 5.
6. 6.
Statements Reasons
1. A is the midpoint of 𝐵𝐸 1. Given D is the midpoint of 𝐶𝐹
2. 2.
3. 𝐵𝐸 𝐶𝐹 3.
4. 4.
A
C
B
D E
F
G
Statements Reasons
1. 1. Given
2. 2. Multiplication Post.
3. 𝐴𝐷 𝐴𝐵 3. Given
4. 𝐴𝐷 𝐷𝐺 4.
5. D is the midpoint of 𝐴𝐺 5.
When a student completed this proof,
they incorrectly identified the reason in
step #2 as Addition Postulate.
Why do you think they thought it was
the Addition Postulate?__________________
_____________________________________________
_____________________________________________
What is the correct postulate that
should be used in reason #2?
_____________________________________________