Aim: What are the congruence shortcuts?

11.14.12

Side-Side-Side Triangle Postulate(SSS)- If 3 sides of a triangle are congruent to 3 sides of another triangle, those two triangles are congruent.

Side-Angle-Side Triangle Postulate(SAS)-If 2 sides of a triangle and the INCLUDED ANGLE are congruent to the 2 sides of another triangle and its INCLUDED ANGLE, then the two triangles are congruent.
* Congruent angle must be between the congruent sides.

Angle-Side-Angle Congruence Postulate(ASA)-Triangles are congruent if any two angles and their INCLUDED SIDE are equal in both triangles.

Angle-Angle-Side Congruence Postulate(AAS)- Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

What "congruence shortcuts" dont work on triangles?

Aim: How do we use the triangle inequality theorem?

11.5.12

Triangle Inequality Theorem: The sum of any 2 sides of a triangle must be greater than the measure of the third side.

Example: 

Side AB is 25

Side BC is 30

Side AC is 50

The sum of AB and BC is greater than AC.

Is there a similar theorem for angle in a triangle?