Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 13: Triangles 171

An isosceles triangle has two sides that are the same length. The congruent sides are called the legs,

and the third side is the base. The angle between the equal sides is the vertex angle, and the other

two angles are base angles.

In an isosceles triangle, the altitude drawn from the vertex to the base bisects the base and the
vertex angle. This is one of the few cases where one line segment does more than one job. It’s an
altitude, it’s an angle bisector, and it’s a median.

An equilateral triangle is one in which all three sides are the same length. All three angles will
be the same size, and because the three angles add up to 180r, each of the angles in an equilateral
triangle measures 60r. Any altitude is a super segment that bisects the side to which it is drawn
and the angle from which it is drawn.

A triangle in which all three sides are the same length is an equilateral triangle. Equilateral

triangles are also equiangular.

Because the three angles of an equilateral triangle are congruent, it is also described as
equiangular. All three angles in an equiangular triangle measure 60r.

WORLDLY WISDOM

Is an equilateral triangle isosceles? It depends on who you talk to. Some folks will say

an isosceles triangle has exactly two equal sides, so they would say no. Others will say an

isosceles triangle has at least two equal sides, and their answer would be yes. The fact is,

anything that’s true for an isosceles triangle is true for an equilateral triangle.

The other ways that triangles are classified by angles have to do with the sizes of the angles. If all
three angles are acute angles, that is, if all three have measurements less than 90r, then you say
the triangle is an acute triangle. This can happen in a scalene triangle if, for example, it has angles
of 80r, 47r, and 53r, or it can happen in an equilateral triangle that has angles of 60r, 60r, and 60r.
An isosceles triangle can be acute, too. For example, you might have angles of 30r, 75r, and 75r.

a

a

Vertex

Vertex

angle

Base

Base angle Base angle

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b

b

a aa

a

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