Third Angle Conjecture














The interior angles for a triangle:  The interior angles of a trianglehave a sum of 180 degrees.






 The Isosceles Triangle:   In an isosceles triangle, the base angles are congruent.                


Triangle Inequalities: 
Any side of a triangle is always shorter than the sum of the two other sides. A triangle cannot be constructed from three segments if any one of them is longer than the sum of the other two.

Angles exterior to a triangle:
An exterior angle is an angle between one side of a triangle and the extension of an adjacent side. The measure of an exterior angle is equal to the sum of the remote interior angles.


Congruent Triangles
Congruent triangles have the same size and shape. That means corresponding sides and corresponding angles are congruent (CPCTC). Triangles are congruent if SSS, SAS, ASA, AAS, or  HL hold true.




Given that triangle LAI is isosceles with vertex A, prove that segment RD and segment ZD are congruent.  Write your proof as a paragraph.