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Geometry
4-4
4-5
4-6
PROVING TRIANGLES CONGRUENT – SSS, SAS
PROVING TRIANGLES CONGRUENT – ASA, AAS
ISOSCELES AND EQUILATERAL TRIANGLES
HOMEWORK #1 Answer Key
I. 1) x = 12
2) x = 5
3) x =
II.
31
6
y=
65
2
Complete each of the following proofs.
1)
Given:
RI and EL bisect each other
Prove:
RDE  IDL
I
E
D
R
Statements
1. RI and EL bisect each other
2.
ED  DL
L
Reasons
1. Given
2. Definition of segment bisector
RD  DI
3. EDR  LDI
3. Vertical angles are congruent
4. RDE  IDL
4. SAS
MPH/KAL 12/14
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2)
Given:
Geometry
E
S is the midpoint of EN
L
SE ^ EL
SN^ NO
Prove:
S
ON@ EL
O
Statements
1)
S is mdpt of EN
N
Reasons
1) Given
SE ^ EL , SN^ NO
2)
ES  NS
2)
3)
E and N are right s
3) Definition of perpendicular lines
4)
E  N
4) All right angles are congruent
5)
OSN  LSE
6)
6)
 NSO   ESL
6) ASA
7)
ON  EL
7) CPCTC
MPH/KAL 12/14
Def of mdpt
Vertical s 
2
3)
Given:
E
Geometry
D
L
G  L
ED bisects GEL
Prove:
D is the midpoint of GL
Hint: If you put all the givens in step one, this can
be completed in six steps.
Statements
1)
G  L
G
Reasons
1) Given
ED bisects GEL
2)
ED  ED
2)
3)
GED  LED
3) Definition of angle bisector
4)
 GED   LED
4) AAS
5)
GD  DL
5)
6)
D is the midpoint of GL
6) Definition of a midpoint
MPH/KAL 12/14
Reflexive Property
CPCTC
3
Geometry
4)
Given:
W
S
WN bisects SWO
Prove:
WSN  WON
N
O
W
Hint: If you put all the givens in step one, this can be
completed in six steps.
Statements
1)
W
Reasons
1) Given
WN bisects SWO
2)
SW  WO
2)
3)
NW  NW
3) Reflexive Property
4)
SWN  NWO
4) Definition of Angle Bisector
5)
 SWB   OWN
5)
6)
WSN  WON
6) CPCTC
MPH/KAL 12/14
All radii of W are 
SAS
4
Geometry
4-4
4-5
4-6
PROVING TRIANGLES CONGRUENT – SSS, SAS
PROVING TRIANGLES CONGRUENT – ASA, AAS
ISOSCELES AND EQUILATERAL TRIANGLES
HOMEWORK #2
I.
Determine if the two triangles are congruent. If the triangles are congruent,
identify which postulate/theorem supports your conclusion and find x and y.
I. 1) AAS or HL - y = 30; x = 2
3)AAS - y = 15; x = 5
1)
Given:
2) SAS - x = 26; y = 16
4) SAS or AAS – x = 19; y = 23
C and D are right angles
AB bisects DAC
Prove:
CB  DB
Statements
1)
C and D are right angles
Reasons
1) Given
AB bisects DAC
2)
C  D
2) All right angles are congruent
3)
1  2
3) Definition of angle bisector
4)
AB  AB
4) Reflexive Property
5)
 DBA   CBA
6)
6)
CB  DB
6) CPCTC
MPH/KAL 12/14
AAS
5
Geometry
2)
Given:
I
H
H and Y are right angles
1
HA  IY
Prove:
1  3
A
Statements
1)
2
H and Y are right angles
43
Y
Reasons
1) Given
HA  IY
2)
H  Y
2) All right angles are congruent
3)
AI  AI
3) Reflexive Property
4)
HAI  YIA
4) HL Theorem
5)
1  3
5) CPCTC
MPH/KAL 12/14
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Geometry
MPH/KAL 12/14
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3)
Given:
I
H
H and Y are right angles
1
HI || AY
Prove:
2
HA  IY
A
Statements
1)
Geometry
H and Y are right angles
43
Y
Reasons
1) Given
HI || AY
2)
H  Y
2) All right angles are congruent
3)
1  3
3) Alternate interior angles theorem
4)
AI  AI
4) Reflexive Property
5)
HIA  YAI
5) AAS
6)
HA  IY
6) CPCTC
MPH/KAL 12/14
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Geometry
4)
Given:
W
S
WN  SO
Prove:
N is the midpoint of SO
Statements
1)
W
N
O
W
Reasons
1) Given
WN  SO
2)
SNW and WNO are right angles
2) Definition of Perpendicular Lines
3)
SNW  WNO
3) All right angles are congruent
4)
SW  OW
4) All radii of a circle are congruent
5)
NW  NW
5) Reflexive Property
6)
SNW  ONW
6) HL Theorem
7)
SN  NO
7) CPCTC
8)
N is the midpoint of SO
8) Definition of a Midpoint
MPH/KAL 12/14
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