TRIANGLE CONGRUENCE PROOFS
Level 1
Prove: ACB FDE
1. Given the following diagram:
C
D
B
E
A
F
2. Given the following diagram:
R
E
A
P
3. Given: XE is a median in XMY and XY XM
Prove: XEM XEY
Prove: ARE PRE
G
4. Given: GH
IH ; JH IG
Prove: ∆JGH≅∆JIH
H
J
I
5.
M
L
Given:
Prove:
KLP MNP ; P is the midpoint of KM
KPL MPN
P
K
N
Prove: O N (Hint: First prove the
triangles are congruent)
6. Given the following diagram:
A
Y
O
M
B
N
Level 2
1.
Given: Circle C with BD and AE as diameters.
A
D
Prove:
ACB DCE
C
B
E
2.
P
Given: PY bisects TPA and TYA
Prove: PTY PAY
T
A
Y
Prove: ABC EDC
3. Given the following diagram:
A
B
C
D
E
4. Given: Circle with center R, YBR RNO.
BRNR
Prove:
N
Y
R
B
5.
L
I
O
N
Given:
LEI NEI , EI
Prove:
LI NI
is an altitude.
E
6. Given: E is the midpoint of
HF and EG
is perpendicular to
HF .
Prove:
HG FG
Level 3
E
1. Given: ABC is equilateral,
EBA DCA
Prove: EB DC.
D
A
B
C
2.
Given: VW WX, VY XZ
Prove: WYZ is isosceles
V
Y
W
Z
X
3.
Given: WZ WX and ZY XY
Prove: ZAY XAY
W
Z
X
A
Y
4.
H
T
S
M
A
Given:
AT MH ; AT
Prove:
ST SM
||
MH
0