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.

2. Now we know that all parts are congruent

1. Prove Triangles Congruent

CPCTC(Corresponding Parts of Congruent Triangles are Congruent

AD

C

B

Given: AB CB

AD CD

Prove: ےA

Cے

=

=

=

• Statement Reason

1) AB = CB, AD = CD 1) Given

2) 2) Reflexive Property

4)

CBDABD

4) CPCTC

BD = BD

3) 3) SSS

AD

C

B

= Aے

Cے

Prove: ےA

Cے

=

A

D

C

B

Given: AF CF

BF DF

Prove:

F

AB = CD

=

=

• Statement Reason

1) AF = CF, BF = DF 1) Given

2) 2) Vertical Angles Theorem

4)

CDFABF

4) CPCTC

CFD ے = AFB ے

3) 3) SAS

A

D

C

B

F

AB = CD

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˚