Learning Target #6 Proving Two Triangles Are Congruent
1
Methods to Prove 2 Triangles are Congruent:
#1 S
S
S
#2 S
A
S
#3 A
S
A
#4 A
A
S
Two methods that do not work:
#1
#2
2
#1: SSS (Side­Side­Side)
Q
M
P
N
#2: Side­Angle­Side (SAS)
Q
P
S
R
X
S
W
Y
3
#3: Angle­Side­Angle (ASA)
B
A
C
E
D
#4: Angle­Angle­Side (AAS)
F
L
I
G
H
J
K
4
Recall previous properties:
Reflexive
Transitive
5
Is it possible to prove the triangles are congruent? If so, how?
a. H
E
G
J
F
b.
N
Q
P
M
c.
U
1
4
W
3
Z
2
X
6
ASSIGNMENT
p. 216 #12­17
p. 223 #8­13
7
Given: KM ≅ NP
KL ≅ NM
LM ≅ MP
Prove: ΔKLM ≅ ΔNMP
*4 steps
Statements
K
N
L
M
P
Reasons
8
Given: BE ≅ CE
AE ≅ DE
Prove: ΔABE ≅ ΔDCE
*4 steps
Statements
B
C
1
E
2
D
A
Reasons
9
Given: AD || EC, BD ≅ BC
Prove: ΔABD ≅ ΔEBC
C
A
B
*5 steps
D
Statements
E
Reasons
10
*On worksheet
Given: AB ≅ DC, E is the midpoint of BC and AD
B
A
E
Prove: ΔAEB ≅ ΔDEC
7 steps
Statements
Reasons
C
D
11
K
Given: FH || LK, GF ≅ GL
Prove: ΔFGH ≅ ΔLGK
F
G
L
*3 ways, 5 steps
H
Statements
Reasons
12
S
R
Given: SV ≅ TV, S ≅ T
Prove: ΔSVR ≅ ΔTVU
*4 steps
Statements
V
U
T
Reasons
13
Given: DR AG
RA ≅ RG
Prove:
ΔDRA ≅ ΔDRG
*6 steps
Statements
1. ______________
2. ______________
3. ______________
4. DRA ≅ DRG
5. DR ≅ DR
6. ______________
Reasons
1. ________________
2. ________________
3. 2 lines , form 4 right angles
4. ________________
5. ________________
6. ________________
14
E
≅ D, AE ≅ BD, AE || BD
Prove: ΔAEB ≅ ΔBDC
A
*5 steps
D
Given: E Statements
B
C
Reasons
15
B
C
Given: AB || CD, BC || DA
Prove: AB ≅ CD
A
Statements
1. 2. 3. 4. 1.
2. 3. AIA
4. AIA
5. BD ≅ BD
6. 5. 6. ASA
7. AB ≅ CD
7.
D
Reasons
16
ASSIGNMENT
Ch. 4 L.T. #6 Practice
17