Isoceles Triangles

Isoceles Triangles are triangles in which at least two sides are congruent.  The two sides tha are congruent are called the legs of the isoceles triangle.  the other side is called the base.  The two angles that touch the base are called the base angles, the other angle is called the vertex angle.

A

B                                     C

Theorem If two sides of a triangle are congruent, the angle opposite the sides are congruent.  Here is how we can prove this theorem: Given: AB is congruent to           AC. Prove:  Angle B is congruent            to angle C. Statements                                     Reasons 1...........................                      1. Given   2. BC is congruent to BC.             2. Reflexive 3. Triangle ABC is congruent        3. SSS to traingle ACB.      4. Angle B is congruent to            4. CPCTC   angle C  This theorem means that the base angles of an isoceles triangle are congruent.  You can also use the converse of this theorem to prove an isoceles triangle.