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Congruent Triangles

Congruent figures◦ They have exactly the same shape.
◦ All parts of one figure are congruent to the
corresponding parts of the other figure.
◦ Corresponding sides and angles are congruent.
B
A
E
C
D
F

Name the congruent triangles.
E
C
D
B
F
A

Find x and y.
ABCD  FGHK
B
C
G
H
136
3x -6 in.
9 in.
A
80
44
D
4x +2y
F
K

If 2 angles of one triangle are congruent to 2
angles of another triangle, then the third
angles are also congruent.
Find mYXW.
X
35
Y
40
W
Z
Prove: ACD  CAB
Given: AD  CB, DC  BA, ACD  CAB, CAD  ACB
A
D
B
C

Side-Side-Side Congruence Postulate- If 3
sides of one triangle are congruent to 3 sides
of a second triangle, then the two triangles
L
are congruent.
N
K
M

Side- Angle- Side Congruence Postulate – If
2 sides and the included angle of one triangle
are congruent to 2 sides and the included
angle of a second triangle, then the 2
triangles are congruent.
Given: KM MN,ML bisects KMN
Prove: KML NML
K
L
M
N

R is the center of the circle. Based on the
diagram, what can you conclude about ∆URT
and ∆SRT ?
S
T
R
U
B
A
D
C

If the hypotenuse and a leg of a right triangle
are congruent to the hypotenuse and a leg of
a second triangle, then the 2 triangles are
congruent.
D
A
B
C
F
E
Given: WY  XZ, WZ  ZY, XY  ZY
W
X
Z
Y
Prove:
WYZ 
XZY

Angle- Side- Angle Congruence PostulateIf 2 angles and the included side of one
triangle are congruent to 2 angles and the
included side of a second triangle, then the 2
triangles are congruent.
Angle- Angle- Side Congruence TheoremIf 2 angle and a non-included side of one
triangle are congruent to 2 angles and the
corresponding non-included side of a second
triangle, then the two triangles are
congruent.

Right Angle Congruence Theorem- All right
angles are congruent.
C
D
B
Given: CBFCDF, BF FD
Prove: ABF EDF
F
A
E

CPCTC- Corresponding Parts of Congruent
Triangles are Congruent