Proving Segment & Angle Relationships
GeorgeBobinson
Segment_Angle_Proofs_Assignment1.docPROVING SEGMENT & ANGLE REALTIONSHIPS ASSIGNMENT
Complete each of the following proofs.
Proof #1
Given:
A
Ð
andB
Ð
are supplementary.B
Ð
andC
Ð
are supplementary.Prove:
C
A
Ð
@
Ð
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STATEMENTS |
REASONS |
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A Ð andB Ð are supplementary.
B Ð andC Ð are supplementary. |
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o B m A m 180 = Ð + Ð
o C m B m 180 = Ð + Ð |
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C m B m B m A m Ð + Ð = Ð + Ð |
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C m A m Ð = Ð |
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C A Ð @ Ð |
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Proof #2
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Given: Lines k and m intersect. Prove: 3 1 Ð @ Ð and4 2 Ð @ Ð
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STATEMENTS |
REASONS |
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Lines k and m intersect. |
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1 Ð and2 Ð form a linear pair
2 Ð and3 Ð form a linear pair
3 Ð and4 Ð form a linear pair |
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1 Ð and2 Ð are supplementary
2 Ð and3 Ð are supplementary
3 Ð and4 Ð are supplementary |
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o m m 180 2 1 = Ð + Ð
o m m 180 3 2 = Ð + Ð
o m m 180 4 3 = Ð + Ð |
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3 2 2 1 Ð + Ð = Ð + Ð m m m m
4 3 3 2 Ð + Ð = Ð + Ð m m m m |
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3 1 Ð = Ð m m
4 2 Ð = Ð m m |
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3 1 Ð @ Ð and4 2 Ð @ Ð |
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Proof #3
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Given: WX = YZ Prove: WY = XZ |
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STATEMENTS |
REASONS |
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WX = YZ |
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WX + XY = XY + YZ |
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WX + XY = WY XY + YZ = XZ |
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WY = XZ |
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Proof #4
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Given: 20 2 1 + = Ð x m ,15 3 2 - = Ð x m and l is a perpendicular bisector of m.Prove: x = 17 |
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STATEMENTS |
REASONS |
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20 2 1 + = Ð x m
15 3 2 - = Ð x m |
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l is a perpendicular bisector of m |
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1 Ð m +2 Ð m = 90 |
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(2x + 20) + (3x – 15) = 90 |
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5x + 20 – 15 = 90 |
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5x + 5 = 90 |
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5x + 5 – 5 = 90 - 5 |
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5x = 85 |
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(5x)/5 = (85)/5 |
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x = 17 |
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Proof #5
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Given: B is the midpoint of AC ,AB = 8x + 44 and BC = 28 Prove: x = -2 |
HINT: Draw a picture.
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STATEMENTS |
REASONS |
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Find the measure of each lettered angle.
a =
b =
c=
d =
e =
