1. Isosceles Triangles, Corollaries, & CPCTC

2. Corresponding parts of congruent triangles are congruent.

3. Corresponding Parts of Congruent Triangles are Congruent.
CPCTC
If you can prove congruence using a shortcut, then you KNOW that the remaining corresponding parts are congruent.
You can only use CPCTC in a proof AFTER you have proved congruence.

4. Corresponding parts
When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are congruent,
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 congruent. A C B G E F
That means that EG  CB FE
What is AC congruent to?

5. For example: Prove: AB  DE A Statements Reasons B C AC  DF Given
<C  <F Given
CB  FE Given
ΔABC  ΔDEF SAS
AB  DE CPCTC D F E

6. Get: a piece of patty paper a straight edge your pencil your compass We are going to create an isosceles triangles with 2 congruent sides.

7. Isosceles Triangles 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.

8. The bisector of the vertex angle of an isosceles Δ is the perpendicular bisector of the base.
In addition, you just learned that the angles opposite congruent sides are congruent…
Vertex angle
Base

9. Your assignment
4.4 Practice Worksheet
4.5 Practice Worksheet