Proving Segment & Angle Relationships

GeorgeBobinson
Segment_Angle_Proofs_Assignment1.doc
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PROVING SEGMENT & ANGLE REALTIONSHIPS ASSIGNMENT

Complete each of the following proofs.

Proof #1

Given:

image1.wmf

A

Ð

and
image2.wmf

B

Ð

are supplementary.
image3.wmf

B

Ð

and
image4.wmf

C

Ð

are supplementary.

Prove:

image5.wmf

C

A

Ð

@

Ð

STATEMENTS

REASONS

image6.wmf

A

Ð

and
image7.wmf

B

Ð

are supplementary.

image8.wmf

B

Ð

and
image9.wmf

C

Ð

are supplementary.

image10.wmf

o

B

m

A

m

180

=

Ð

+

Ð

image11.wmf

o

C

m

B

m

180

=

Ð

+

Ð

image12.wmf

C

m

B

m

B

m

A

m

Ð

+

Ð

=

Ð

+

Ð

image13.wmf

C

m

A

m

Ð

=

Ð

image14.wmf

C

A

Ð

@

Ð

Proof #2

Given: Lines k and m intersect.

Prove:

image15.wmf

3

1

Ð

@

Ð

and
image16.wmf

4

2

Ð

@

Ð

image17.png

STATEMENTS

REASONS

Lines k and m intersect.

image18.wmf

1

Ð

and
image19.wmf

2

Ð

form a linear pair

image20.wmf

2

Ð

and
image21.wmf

3

Ð

form a linear pair

image22.wmf

3

Ð

and
image23.wmf

4

Ð

form a linear pair

image24.wmf

1

Ð

and
image25.wmf

2

Ð

are supplementary

image26.wmf

2

Ð

and
image27.wmf

3

Ð

are supplementary

image28.wmf

3

Ð

and
image29.wmf

4

Ð

are supplementary

image30.wmf

o

m

m

180

2

1

=

Ð

+

Ð

image31.wmf

o

m

m

180

3

2

=

Ð

+

Ð

image32.wmf

o

m

m

180

4

3

=

Ð

+

Ð

image33.wmf

3

2

2

1

Ð

+

Ð

=

Ð

+

Ð

m

m

m

m

image34.wmf

4

3

3

2

Ð

+

Ð

=

Ð

+

Ð

m

m

m

m

image35.wmf

3

1

Ð

=

Ð

m

m

image36.wmf

4

2

Ð

=

Ð

m

m

image37.wmf

3

1

Ð

@

Ð

and
image38.wmf

4

2

Ð

@

Ð

Proof #3

Given: WX = YZ

Prove: WY = XZ

image39.png

STATEMENTS

REASONS

WX = YZ

WX + XY = XY + YZ

WX + XY = WY XY + YZ = XZ

WY = XZ

Proof #4

Given:

image40.wmf

20

2

1

+

=

Ð

x

m

,
image41.wmf

15

3

2

-

=

Ð

x

m

and l is a perpendicular bisector of m.

Prove: x = 17

image42.png

STATEMENTS

REASONS

image43.wmf

20

2

1

+

=

Ð

x

m

image44.wmf

15

3

2

-

=

Ð

x

m

l is a perpendicular bisector of m

image45.wmf

1

Ð

m

+
image46.wmf

2

Ð

m

= 90

(2x + 20) + (3x – 15) = 90

5x + 20 – 15 = 90

5x + 5 = 90

5x + 5 – 5 = 90 - 5

5x = 85

(5x)/5 = (85)/5

x = 17

Proof #5

Given: B is the midpoint of

image47.wmf

AC

,

AB = 8x + 44 and BC = 28

Prove: x = -2

HINT: Draw a picture.

STATEMENTS

REASONS

Find the measure of each lettered angle.

image48.png

a =

b =

c=

d =

e =

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