Isosceles Triangle - Angles

Date: 11/6/96
From: Michelle
Subject: Geometry

Given that one base angle of an isosceles triangle is 39 degrees, find 
the measure of the other two angles in the triangle.

Date: 11/07/96 at 12:46:30
From: Doctor Wilkinson
Subject: Re: Geometry

To start, let's make sure you understand the definitions of the terms.

As isosceles triangle has two congruent sides with a third side 
that is the base.

A base angle of an isosceles triangle is one of the angles formed by
the base and another side.  Base angles are equal because of the 
definition of an isosceles triangle.

A picture would probably help here:


                        A
                        .
                       / \              ABC = ACB = 39 degrees
                      /   \             BAC = ??
                     /     \
                    /       \
                   /         \
                  /           \
                 /             \
                ._______________.
               B                 C
                      base

ABC is the isosceles triangle.  AB is congruent to AC.  Angle ABC
is congruent to angle ACB.  These are the base angles.

Now let's look at what we're given and what we're asked to find out.

We're given that one of the base angles is 39 degrees.  We know that
the base angles are congruent, so we actually know both base angles
are 39 degrees: that is, we know that angle ABC and angle ACB are
both 39 degrees.  We're asked to find out the measures of the other 
two angles, and we've already got one of them, so all we need to find 
out is the measure of angle BAC.

We know two out of the three angles, but we've used up the specific 
information we were given.  Now we need to look for some general rule 
that will connect the unknown (the angle BAC) to the known (the angles 
ABC and ACB).  Do you know such a rule?

Now it's your turn.  If you're still stuck, let me know.

-Doctor Wilkinson,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/