A square on its corner
A square has four straight sides, all the same length, and four square corners. Most pictures show it sitting flat on one side.
Now stand the same square on one of its corners. Many people call it a diamond, but nothing about it has changed. No side was added or taken away, and no side got longer or shorter. It still has four equal sides and four square corners, so it is still a square. Only the way it faces has changed.
A square sitting flat on one side.
The same square, turned to stand on a corner. It still has four equal sides and four corners.
Bigger or smaller
Shrink the square and it is smaller, but its four sides are still straight and still all the same length. So it is still a square. The same is true when a shape is made bigger. The size of a shape does not change its name.
A smaller square, still standing on a corner. Its four sides are still equal.
Turn it and count
Turning works the same way for every shape. A triangle that points down has three straight sides and three corners, just like one that points up, so it is a triangle. A rectangle stood on its short side still has two long sides and two short sides, so it is still a rectangle.
Watch the sides and corners while the shape turns: none appears and none disappears. That is why the name stays the same.
turned 0°, still a triangle: sides = corners = 3, unchanged; the name depends on the sides and corners, not on which way up it sits
Turn it upside down: is it still the same shape?
Turn the shape with the handle, or pick a rectangle or a long rectangle. The dashed outline shows where it started; however far it turns, the count of sides and corners stays the same.
Name it by its sides
So when a shape sits at a slant, is very small, or is long and thin, do not name it by how it looks at first glance. Count its straight sides and look at their lengths, and name it from that.
Worked example: Triangles That Point Up, Point Down and One Tiny Triangle
Question Mei draws 3 triangles that point up and 2 triangles that point down. She draws 1 tiny triangle that points to the side. She also draws 2 squares. (a) How many triangles does Mei draw in all? (b) How many shapes does Mei draw in all?
1.Draw every shape: 3 triangles that point up, 2 that point down, 1 tiny triangle and 2 squares.
There are 3 triangles that point up, 2 that point down, 1 tiny triangle and 2 squares. 2.A triangle has 3 straight sides and 3 corners. It is still a triangle when it is turned or made smaller.
A triangle has 3 straight sides and 3 corners. It is still a triangle when it is turned or made smaller. 3.(a) Count the triangles: 3 + 2 + 1 = 6. Mei draws 6 triangles in all.
(a) Count the triangles: 3 + 2 + 1 = 6. Mei draws 6 triangles in all. 4.(b) Count the 2 squares as well: 6 + 2 = 8. Mei draws 8 shapes in all.
(b) Count the 2 squares as well: 6 + 2 = 8. Mei draws 8 shapes in all.
Answer: (a) 6 triangles; (b) 8 shapes
Common mistakes
- Saying that the triangles that point down are not triangles. A shape with 3 straight sides and 3 corners is a triangle, whichever way it points.
- Leaving out the tiny triangle. A small triangle is still a triangle, so count it.
More shapes and where they sit problems, worked step by step →