The document discusses proofs involving congruent triangles. It defines congruent triangles as having congruent angles and sides. The main methods of proof are: using the definition of congruent triangles and corresponding parts of congruent triangles (CPCTC); using angle-side-angle (ASA) and side-side-side (SSS) postulates; and applying theorems like the isosceles triangle theorem and base angles theorem. Examples of congruent triangle proofs are provided to solve for specific angle or side measures.

1. Ch4.3_CongruentTrianglesProofs.notebook October 24, 2011
1

2. Ch4.3_CongruentTrianglesProofs.notebook October 24, 2011
Chapter 4.3
Congruent Triangles
Continuing Proofs
2

3. Ch4.3_CongruentTrianglesProofs.notebook October 24, 2011
Congruent triangles have
congruent angles and
congruent sides
C.P.C.T.C.
Corresponding
Parts of
Congruent
Triangles are
Congruent
s or angles)
(s egment
Prove corresponding parts are equal
3

4. Ch4.3_CongruentTrianglesProofs.notebook October 24, 2011
C.P.C.T.C.
AC ≅ AC Reflexive
SSS
CPCTC
4

5. Ch4.3_CongruentTrianglesProofs.notebook October 24, 2011
C.P.C.T.C.
Prove: VX ≅ ZX
Statement Reason
Definition of
perpendicular
lines
Transitive
Property
ΔVXW ≅ ΔZXY ASA
VX ≅ ZX
5

6. Ch4.3_CongruentTrianglesProofs.notebook October 24, 2011
Isosceles Triangle Theorem
es
sid
nt
rue
o ng B
2 c B
Then
If
A C A C
If 2 sides of a triangle are ≅,
then the angles opposite
from them are also ≅
Base Angles Theorem
Converse of Isosceles Δ thm.
If 2 angles of a triangle are ≅,
then the sides opposite
from them are also ≅
B B
A C A C
Examples:
Solve for X
X
660
Solve for A and B
A 3 in
B
2 c Solve for X, Y, and Z
X m
2 cm Z
m
Y 2 c
Solve for X and Y
0
60 Y
X
3.4 ft
Solve for X
X
1100
700
6

7. Ch4.3_CongruentTrianglesProofs.notebook October 24, 2011
Page 162
#1­11, 18
7