We just worked a little with triangles. But what is a “triangle”? Which of the following should be considered a triangle and why?

From examining these figures, come up with a definition of “triangle”. That is, what criteria should a figure satisfy in order to be a member of the “club” of triangles?

You may recall from school that there are some special triangles that fulfill even more criteria than the basic definition on our previous page. Try to recall what it means for a triangle to be equilateral, isosceles, scalene, right, acute, or obtuse. Then decide whether or not the following triangles are possible.
(a)
An equilateral right triangle
(b)
An isosceles triangle that is obtuse.
(c)
A scalene triangle in which at least two angles are the same.
(d)
An acute right triangle.
(e)
A triangle with two right angles.

We now move on to another kind of polygon: the quadrilateral.

These figures are quadrilaterals:

These figures are not quadrilaterals:

From examining these figures, come up with a definition of a “quadrilateral”. What should be the definition of a “polygon”?
2025-09-03 01:07:34