Transcript 2-7 Proving Segment Relationships

2-7 Proving Segment Relationships
Ms. Andrejko
Real World
Postulates/Theorems
 Ruler postulate
 Segment addition postulate
 Reflexive property
 Symmetric property
 Transitive property
Examples
 Justify each statement with a property of equality, a property
of congruence, or a postulate.
1.
QA = QA
Reflexive property of equality
2.
If AB ≅ BC and BC ≅ CE then AB ≅ CE
Transitive property of congruence
Examples
 Justify each statement with a property of equality, a property
of congruence, or a postulate.
1.
If Q is between P and R, then PR = PQ + QR.
Segment addition postulate
2.
If AB + BC = EF + FG and AB + BC = AC, then EF + FG = AC
Transitive property of equality
Example- Complete the Proof
STATEMENTS
Given: SU  LR
SU≅LR, TU≅LN
TU  LN
Prove: ST  NR
.. . . ..
S

L
T
N
U
R
SU =LR , TU=LN
SU = ST+ TU
LR= LN+NR
REASONS
GIVEN
Definition of congruent
segments
Segment + post.
ST+TU = LN+NR
Substitution Prop.
ST+LN = LN+NR
Substitution prop.
ST+LN-LN=LN+NR-LN
Subtraction Prop.
ST = NR
Substitution Property
ST ≅ NR
Def. of congruent
Practice
STATEMENTS
AB ≅ CD
AB = CD
CD = AB
CD ≅ AB
REASONS
Given
Def. of congruent
Symmetric
Definition of
congruent segments

Practice- Complete the Proof
STATEMENTS
Given: LK  NM
KJ  MJ
Prove: LJ  NJ
LK ≅ NM, KJ ≅ MJ
LK = NM, KJ = MJ
LK + KJ = NM + MJ
LJ = LK+KJ,
NJ=NM+MJ
REASONS
GIVEN
Definition of congruent
segments
Add. Prop.
Segment addition post.
LJ = NJ
Substitution prop.
LJ ≅ NJ
Def. of congruent
Example: Fill in the proof
Given: WX  YZ
W
Y
X
Prove: WY  XZ

STATEMENTS
WX ≅YZ
 WX = YZ
XY = XY
WX +XY = YZ +XY
WY= WX+XY
XZ = YZ+XY
WY = XZ
WY ≅ XZ
REASONS
Given
Def. of congruence
Reflexive Prop.
Additive Prop.
Segment addition post.
Substitution
Def. of Congruence
Z
Practice: Fill in the proof
Given: X is the midpoint of SY S
Z is the midpoint of YF
XY = YZ
Prove: ZF ≅ SX
STATEMENTS
X is the midpoint of SY
Z is the midpoint of YF
XY = YZ
XY ≅YZ
SX≅ XY ; YZ ≅ ZF
SX ≅YZ
SX ≅ ZF
ZF ≅ SX
F
X
Z
Y
REASONS
Given
Def. of Congruence
Def. of Midpoint
Substitution
Transitive Prop.
Symmetric