4.3-4.5 In Class Worksheet
Decide whether you can deduce by the SSS, SAS, or
ASA Postulate that another triangle is congruent to
ABC. If so, write the congruence and name the
postulate used. If not, write no congruence. WRITE
YOUR ANSWERS ON THIS SHEET.
1. A
A
2.
C
D
B
B
ASA
ABC≅ NPY
P
Y
N
C
5.
C
SSS KAC≅ BCA
X none
S
SAS
BAC≅ BSC
B
A
B
4. A
C
3.
K
SAS
BCA≅ DCA
A
NONE
6.
B
A
Y
7.
A
C
C
Z B
SAS
ABC≅ PQC
J
P
8. A
NONE
P
C
C
B
Q
B
Q
C
9.
60
10.
B
0
B
A
61o
59o
G
ASA
BAC≅ DCA
A
ASA
ABC≅ AGC
12.
A
A
11.
B
S
13.
B
T
C
C
B
14.
F
A
NONE
15.
V
C
ASA
ABC≅ BST
D
C
600
U
NONE;not a choice
given but could do
3rd angle thm. A
B
G
C
SAS
ABC≅ CGA
N
C
M
AAS ABC≅ MNC
A
B
D
Proofs
A
E
1. Given: E is midpoint of AB and CD
BED
Prove: AEC ≅ _____
B
C
Given
def of a midpoint
VAT
SAS
E is midpoint of AB and CD
AE= EB; CE=ED
<AEC≅<BED
AEC ≅ BED
P
2. Given: PQ l QR; RS l ST ;
R is midpoint of QS
Q
Prove:
PRQ ≅ _______
TRS
R
S
T
S
1. PQ l QR; RS l ST ;
R is midpoint of QS
2. <Q and <S are rt <'s
3. <Q≅<S
4. QR=RS
5. <PRQ≅<TRS
PRQ ≅
6.
TSR
R
GIVEN
def of l
rt <'s are ≅
def of midpoint
VAT
ASA
A
C
3. Given: <A≅<D; X is midpoint of AD
BXA
Prove: CXD≅ ______
X
B
<A≅<D; X is midpoint of AD
AX=XD
<AXB≅<DXC
CXD≅ BXD
4. Given: MO≅PO ; ON bisects MP
PON
Prove: MON≅ ______
D
Given
def of midpoint
VAT
ASA
M
N
O
MO≅PO ; ON bisects MP
NO ≅ NO
MN ≅ PN
MON≅ PON
Given
Reflexive
def of bisector
SSS
P
V
5. Given: VW≅VZ ; VX≅VY
VZX
Prove: VWY≅ _____
Z
W
X
VW≅VZ ; VX≅VY
<V≅<V
VWY≅ VZX
Y
Given
Reflexive
SAS
6. Draw and label a diagram. List, in terms of the
diagram, what is given and what is to be proved. Then
write a two-column proof.
In an isosceles triangle, if the angle between the
congruent sides is bisected, then two congruent
triangles are formed.
B
AB≅CD, BD bisects <ABC
Given
A
<ABD≅<CBD
def < bisector
BD≅BD
reflexive
ABD≅ CBD
SAS
D
C