Isosceles triangles have at least two congruent sides and at least two congruent angles. The congruent sides, called legs, form the vertex angle. The other two congruent angles are the base angles. Isosceles triangles are used in the regular polygon area formula and isosceles right triangles are known as 45-45-90 triangles.
When we're talking about isosceles triangles there are two key things. The first is isosceles triangles mean we have two sides that are congruent. If we know that we can assume that the base angles are congruent but wait a minute I just used a couple new words. First one was base angles. Our base angles are the two angles that are not part of the vertex but wait a minute, what's the vertex? Well the vertex is this angle right here and notice that the vertex contains the two sides of the triangle that are congruent, so what I said is if you know that two sides of a triangle are congruent then the two base angles must be congruent. If you're interested, you can also call this side here that's opposite the vertex the base. What about the converse? Remember the converse is when you switch the if and the then part of a conditional statement, so over here I've drawn a triangle where you have two base angles that are congruent. Can we assume that this is an isosceles triangle where two sides are congruent? The answer to that is yes. If you know that two base angles are congruent, then it has to be an isosceles triangle with two sides that are congruent.