An equilateral triangle is a special 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 example figure depicts an equilateral triangle with all the parts labeled.
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.
Example:
1. Problem: Find AB and AC on the triangle depicted
in the accompanying 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 tri-
angle (AB and BC) are congruent. There-
fore, 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.
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Take the quiz on isosceles and equilateral triangles. The quiz is very useful for either review or to see if you've really got the topic down.