Types of Triangle
Sorting by sides
Every triangle has three sides, and the first way to sort them is by
which sides are equal:
-
an equilateral triangle has all three sides equal — and,
as a result, all three angles equal too, each exactly
60^\circ;
-
an isosceles triangle has two sides equal (and the two
angles opposite those sides are equal as well);
-
a scalene triangle has no sides equal — every side, and
every angle, a different size.
Sides known to be equal are marked with little tick marks: sides carrying
the same number of ticks have the same length.
Sorting by angles
The second way to sort a triangle is by its biggest angle:
-
an acute triangle has all three angles less than
90^\circ;
-
a right-angled triangle has exactly one
90^\circ angle (marked with a small square);
-
an obtuse triangle has one angle greater than
90^\circ.
Every triangle can be named in two independent ways:
-
by its sides — equilateral (three equal), isosceles (two equal) or
scalene (none equal);
-
by its angles — acute (all angles
< 90^\circ), right-angled (one
= 90^\circ) or obtuse (one
> 90^\circ);
-
because the angles
sum to
180^\circ, a triangle can have at most one
right angle or obtuse angle — two would already total
180^\circ or more.
The whole family
Step through the gallery to meet one of each. The top row is sorted by sides, the bottom row
by angles — but remember the two labels combine, so a single triangle might be, say,
"isosceles and right-angled".