Parallel Lines        Congruent Tri.        Congruent R. Tri.    Isosc. and Equil.        Quadrilaterals        Parallelograms        Ratios        Similar Polygons        Special Triangles       Circles        Area        Coordinate Geo.        Triangle Ineq.        Solids        Computer Fun

On this page we hope to clear up problems that you might have with isosceles and/or equilateral triangles.  These kind of triangles are special triangles, and if you scroll down, you'll be able to better understand the peculiarities of each type of triangle. An isosceles triangle has two congruent sides called legs and a third side called the base.  The vertex angle is the angle included by the legs.  The other two angles are called base angles.  The base angles are congruent.  The figure below depicts an isosceles triangle with all the parts labeled. An equilateral triangle is a special isosceles triangle in which all three sides are congruent.  Equilateral triangles are also equiangular, which means all three angles are congruent.  The measure of each angle is 60 degrees.  The figure below depicts an equilateral triangle with all the parts labeled. There are a few special rules you ought to remember when dealing with isosceles and/or equilateral triangles.  They are outlined below. 1.  If a triangle is equilateral, it is equiangular. 2.  If two angles of a triangle are congruent, they are the base angles of an isosceles triangle. 3.  If a triangle is equiangular, it is equilateral. By keeping those rules in mind and the definitions of isosceles and equilateral triangles in mind, you can solve all kinds of problems. 1. Problem: Find AB and AC on the triangle in the figure. Solution: Since angle A is congruent to angle C (information is given in the figure), segment AC is the base of an isosceles triangle (see Rule 2 above). Because of that, we know that the two legs of the triangle (AB and BC) are congruent. Therefore, AB = 5. We also know that all triangles are made of three angles that have measures that when added together equal 180 degrees. With that information, we can set up an equation to find the measure of angle B. 60 + 60 + B = 180 Solving the equation gives us 60 for B. That tells us that the triangle is equiangular. Rule 3 above says that all equiangular triangles are also equilateral. If the triangle is equilateral, then all the sides have the same measure. Therefore, AC also equals 5. Back to Top  Take the Quiz on isosceles and equilateral triangles.  (Very useful to review or to see if you've really got this topic down.)  Do it!