Geometry Unit 4 Homework Packet Name Unit 4 Homework 1 Unit 04.pdf · Geometry Unit 4 Homework Packet Name_____ Unit 4 Homework 3 #1 – 5: Name the property that justifies the statement

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


#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.


Unit 4 Homework 2



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______________________________


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______________________________


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


c) Given: YZXWXZ

ZXYXZW

Prove: YZWWXY


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:


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.


5. Given:

A 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?

_____________________________________________

Documents

Geometry Unit 4 Homework Packet Name Unit 4 Homework 1 Unit 04.pdf · Geometry Unit 4 Homework Packet Name_____ Unit 4 Homework 3 #1 – 5: Name the property that justifies the statement