Download 3.2 - Congruent Triangles

3.2 ­ Congruent Triangles
October 09, 2015
Congruent Polygons
Congruent Triangles
Congruent Triangles = All pairs of corresponding parts are congruent.
F
C
E
B
• All corresponding sides are congruent
A
All triangles have 6 parts
D
A
3 Sides
• All corresponding angles are congruent
3 Angles
C
B
3.2 ­ Proving Triangles Congruent
Side
Angle
Side
Angle
Side
Angle
Ways to Prove Triangles Congruent (3 Postulates)
Sides
1.) Side­Side­Side (SSS) Postulate
Angles
If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent.
H
A
Side
Angle
Side
Angle
Side
Angle
Reflexive Property
Any segment or angle is congruent to itself.
C
B
F
G
The reflexive property creates a copy of a segment or angle for you to use in two different triangles.
U
W
N
P
Q
X
Y
M
I
P
1
3.2 ­ Congruent Triangles
October 09, 2015
Ways to Prove Triangles Congruent (3 Postulates)
A
2.) Side­Angle­Side (SAS) Postulate
D
If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.
Side
Angle
Side
Angle
Side
Angle
F
A
C
B
E
G
D
C
B
E
J
H
Included angle = The angle formed between the two congruent sides.
K
Ways to Prove Triangles Congruent (3 Postulates)
H
A
3.) Angle­Side­Angle (ASA) Postulate
If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.
Side
Angle
Side
Angle
Side
Angle
Included side = The side between the two congruent angles.
C
B
F
G
V
M
W
O
E
Y
X
N
N
M
P
A
Given:
D midpoint of Ways to Prove Triangles Congruent (3 Postulates)
Prove:
Summary
Statements
1.) SSS (Side­Side­Side)
Reasons
B
D
C
2.) SAS (Side­Angle­Side)
3.) ASA (Angle­Side­Angle)
2