Download Section 4-2 Proving ∆ Congruent

Bell-Ringer
Given: ABC  DEF , m<A = 2x+18,
m<B = 3x+5, m< F = 7x+1
 Find x

Section 4-2
Proving ∆’s Congruent
Goal: Prove two
triangles are congruent.
We are going to
learn 5 ways!!!!
SSS Postulate
If
three sides of one
triangle are congruent to
three sides of another
triangle, then the triangles
are congruent.
SSS
 Side
E
AB
 Side
 EF
 Side
 AC

D
F
B
A
C
 DE
 BC
 DF
SAS Postulate
 If
two sides and the
included angle of one
triangle are congruent to
two sides and the included
angle of another triangle,
then the triangles are
congruent.
SAS
 Side
T
 TO
O
 Angle
M
 <O
P
 Side
 OM
A
T
 PA
 <A
 AT
ASA Postulate
 If
two angles and the
included side of one triangle
are congruent to two angles
and the included side of
another triangle, then the
triangles are congruent.
ASA
A
 Angle
 <L
 Included
R
L
 LR
E
 Angle
N
J
 <J
 <R

Side
JN
 <N
AAS Theorem
 If
two angles and a nonincluded side of one triangle
are congruent to the
corresponding parts of
another triangle, then the
triangles are congruent.
AAS
Angle
 <L  <I
 Angle
 <J  <G
 Non-Included
Side
 JK  GH

L
K
J
I
G
H
HL Theorem
If the hypotenuse and a leg of one right
triangle are congruent to the
corresponding parts of another right
triangle, then the triangle are
congruent.
 Why is it true?

HL
Right Triangle
 Hypotenuse
 LK  IH
 Leg
 JK  GH

L
K
J
I
G
H
There is a strategy that we
want to use when proving that
triangles or parts of triangles
are congruent.
Proving two triangles are
congruent
 Identify
two triangles
 Use your colors to show what is
congruent
 Make a statement for each
congruent piece
 Say the triangles (in correct
order!!) are congruent by…
Proving two segments or two
angles congruent
 Identify
the 2 triangles and
their congruent pieces
 Prove the triangles to be
congruent
 Use CPCTC to prove the
parts congruent.
Let’s Practice!!!!
Homework
Pg 124-125 Written Exercises #1-15
 Pg 142 Classroom Exercises #1-9
