4.4 Isosceles Triangles,Corollaries, &

CPCTC

♥ Has at least 2 congruent sides.

♥ The angles opposite the congruent sides are congruent

♥ Converse is also true. The sides opposite the congruent angles are also congruent.

♥ This is a COROLLARY. A corollary naturally follows a

theorem or postulate. We can prove it if we need to, but it really makes a lot of sense.

Isosceles Triangles

♥ The bisector of the vertex angle of an isosceles Δ is the perpendicular bisector of the base.

Vertex angle

In addition, you just learned that the angles opposite congruent sides are congruent…

Base

Corresponding partsWhen you use a shortcut (SSS, AAS, SAS,

ASA, HL) to show that 2 triangles are ,that means that ALL the corresponding parts

are congruent.

EX: If a triangle is congruent by ASA (for instance), then all the other corresponding parts are .

A

C

B

GE

FThat means that EG CB

What is AC congruent to? FE

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.

If you can prove congruence using a shortcut, then you KNOW that the remaining corresponding parts are congruent.

Corresponding Parts of Congruent Triangles are Congruent.

You can only use CPCTC in a proof AFTER you have proved congruence.

CPCTC

For example:Prove: AB DE

A

F E

D

C B

Statements Reasons

AC DF Given

C F Given

CB FE Given

ΔABC ΔDEF SAS

AB DE CPCTC

Your assignment

2 - Cut and paste proofs2 – DIY proofs3 - Constructions