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
1
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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