Download 4.3 Congruent Triangles and Proofs

4.3 Congruent Triangles
and Proofs
Date:________________

If triangles are congruent, then we can say
that all corresponding parts are congruent.

1. Each corresponding pair of sides are Congruent.
2. Each corresponding pair of angles are Congruent.
To show that two angles (one in each triangle)
are congruent, we only need to prove the
triangles congruent.
1. Prove Triangles Congruent
2. Now we know that all parts are congruent
CPCTC
(Corresponding Parts of Congruent Triangles are Congruent
B
A
C
D
Given: AB = CB
AD = CD
Prove: ‫ے‬A = ‫ے‬C
Prove: ‫ے‬A = ‫ے‬C
B
A
C
D
• Statement
Reason
1) AB = CB, AD = CD 1) Given
2) BD = BD
3)
ABD  CBD
4) ‫ے‬A = ‫ے‬C
2) Reflexive Property
3) SSS
4) CPCTC
A
C
F
B
D
Given: AF = CF
BF = DF
Prove:
AB = CD
C
A
F
B
• Statement
D
Reason
1) AF = CF, BF = DF
1) Given
2) ‫ ے‬AFB =
2) Vertical Angles Theorem
3)
‫ ے‬CFD
ABF  CDF
4) AB = CD
3) SAS
4) CPCTC
TRIANGLE FAST FACTS:
ISOSCELES TRIANGLES: if two sides of a
triangle are congruent, then their opposite angles
are congruent…and vice-versa (both ways).

TRIANGLE FAST FACTS:
ISOSCELES RIGHT TRIANGLES: if a
triangle is isosceles and right, then the other two
angles are always 45˚ .
45˚
45˚
TRIANGLE FAST FACTS:
EQUILATERAL TRIANGLES: if a triangle is
equilateral, then it is equiangular. (all three
angles are equal to 60˚)
60˚

60˚
60˚