NAME
DATE
PERIOD
Skills Practice
Proving Segment Relationships
Justify each statement with a property of equality, a property of congruence, or a
postulate.
1. QA = QA
2. If AB = BC and EC = CE then AB = CE.
3. If Q is between P and R, then PR = PQ + QR.
4. If AB +BC = EF + FG and AB + BC = AC, then EF + FG = AC.
PROOF Complete each proof.
5. Given: SU = LR
TU = LN
Prove: ST = NR
Proof:
s
9L
•-
T
-»
N
a. SU s LR, TU = LN
b.
b. Definition of s segments
c.
c. SU = ST + TU
LR = LN + NR
d.ST
e.ST0!
I
d.
e.
f.
g. Substitution Property
h.
f. ST + LN-LN = LN+ NR - LN
g-
h.sr =
6. Given: AB s CD
Prove: CD s
Proof:
Statements
Reasons
a. Given
b.
a.
b.AB =
c. CD = AB
d.
Chapter 2
R
-•
Reasons
a.
Statements
1
U
•
c.
d. Definition of s segments
45
Glencoe Geometry
NAME
DATE
PERIOD
Word Problem Practice
Proving Segment Relationships
1. FAMILY Maria is 11 inches shorter
than her sister Nancy. Brad is 11 inches
shorter than his brother Chad. If Maria
is shorter than Brad, how do the heights
of Nancy and Chad compare? What if
Maria and Brad are the same height?
4. NEIGHBORHOODS Karla, John, and
Mandy live in three houses that are on
the same line. John lives between Karla
and Mandy. Karla and Mandy live a
mile apart. Is it possible for John to be a
mile from both Karla and Mandy?
2. DISTANCE Martha and Laura live
1400 meters apart. A library is opened
between them and is 500 meters from
Martha.
5. LIGHTS Five lights, A, B, C, D, and E,
I
500 meters
Martha
I
are lined up in a row. The middle light
is the midpoint of the second and fourth
light and also the midpoint of the first
and last light.
1
Library
a. Draw a figure to illustrate the
situation.
Laura
1400 meters
How far is the library from Laura?
b. Complete this proof.
Given; C is the midpoint ofBD
andAE.
Prove: AB = DE
Statement
Reason
1. C is the midpoint 1. Given
ofBD andAE.
3. LUMBER Byron works in a lumber
yard. His boss just cut a dozen planks
and asked Byron to double check that
they are all the same length. The planks
were numbered 1 through 12. Byron
took out plank number 1 and checked
that the other planks are all the same
length as plank 1. He concluded that
they must all be the same length.
Explain how you know plank 7 and
plank 10 are the same length even
though they were never directly
compared to each other?
Chapter 2
47
2. BC = CD and
2.
3. AC = AB + BC,
CE = CD + DE
3.
4. AB = AC - BC
4.
5.
5. Substitution
Property
6. DE = CE- CD
6.
7.
7.
Glencoe Geometry
NAME .
Practice
Word Problem Practice
Proving Segment Relationships
Proving Segment Relationships
Complete the following proof.
1. Given: AB^DE
B is the midpoint of AC.
E is the midpoint of DF.
Prove: BC = EF
Proof:
Statements
Reasons
a./IB 3 DE
B is the midpoint of AC.
E is the midpoint of DF.
b.AB = DE
c./»B = BC
a. Given
b. Definition of = segments
c. Definition of Midpoint
2. DISTANCE Martha and Laura live
1400 meters apart. A library is opened
between them and is 500 meters from
Martha.
5. LIGHTS Five lights, A, B, C, D, and E,
are lined up in a row. The middle light
is the midpoint of the second and fourth
light and also the midpoint of the first
and last light.
500 meters
e. Subs. Prop.
a. Draw a figure to illustrate the
Library
Apex
Redding
Pine Blurt
Given: GAs RP~
Prove: GR s AP
Proof:
Statements
Reasons
^.GA=RP
1. Given
2. GA = RP
2. Definition of s segments
3. GA + AR = AR + RP
3. Add. Prop.
4. GR = GA + AR, AP=AR + RP
4. Seg. Add. Post.
5. Subs. Prop.
5. GR = AP
6. Definition of s segments
46
Glencoe Geometry
How far is the library from Laura?
900m
Light 1
Light 2
Light 3
Light 4
Light 5
b. Complete this proof.
Given: C is the midpoint of BD
andAE
Prove: AB = DE
Statement
Reason
1. C is the midpoint 1. Given
ofBDandAE.
2. BC = CD and
2. Del, of mdpt.
AC = CE
3. LUMBER Byron works in a lumber
yard. His boss just cut a dozen planks
and asked Byron to double check that
they are all the same length. The planks
were numbered 1 through 12. Byron
took out plank number 1 and checked
that the other planks are all the same
length as plank 1. He concluded that
they must all be the same length.
Explain how you know plank 7 and
plank 10 are the same length even
though they were never directly
compared to each other?
Plank 7 is the same length as
plank 1 and plank 1 is the same
length as plank 10. By the
transitive prop., plank 7 must be
the same length as plank 10.
Chapter Z
(D
0)
situation. Sample answer:
f. Definition of a segments
2. TRAVEL Refer to the figure. DeAnne knows that the
Grayson
distance from Grayson to Apex is the same as the distance
G
from Redding to Pine Bluff. Prove that the distance from
Grayson to Redding is equal to the distance from Apex to Pine Bluff.
•ou| 'saiuedwoo IMH-
4. NEIGHBORHOODS Karla, John, and
Mandy live in three houses that are on
the same line. John lives between Karla
and Mandy. Karla and Mandy live a
mile apart. Is it possible for John to be a
mile from both Karla and Mandy?
No, it's not possible. John must
be less than a mile from both of
them since he lives between
them.
d. Subs. Prop.
d.BC = DE
e. BC_= EF
t. BC s EF
Chapter 2
1. FAMILY Maria is 11 inches shorter
than her sister Nancy. Brad is 11 inches
shorter than his brother Chad. If Maria
is shorter than Brad, how do the heights
of Nancy and Chad compare? What if
Maria and Brad are the same height?
Nancy is shorter than Chad when
Maria is shorter than Brad; Nancy
and Chad are the same height
when Maria is the same height as
Brad.
47
3. AC = AB + BC,
CE = CD + DE
4.AB=AC -BC
3. Seg. Add. Post.
6. DE = CE - CD
e.Subtr. Prop.
7.AB = DE
7. Trans. Prop.
4.Subtr. Prop.
5. Substitution
Property
Glencoe Geometry
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