Look around. A window, a cracker, a wheel, and a sign do not all look the same. They have different shapes. Some shapes have straight sides. Some shapes have corners. Some shapes have sides that are the same length, and some have long and short sides.
A shape is a flat figure we can see and name. We can learn about a shape by looking at its sides and its corners. When we talk about shape, we can ask simple questions: How many sides are there? How many corners are there? Are the sides all the same, or are some longer?
Side is a straight edge of a shape.
Corner is a place where two sides meet.
Angle is the turn at a corner. For these shapes, each corner is also an angle.
Some shapes are made of straight sides. A circle is different because it is round and has no straight sides and no corners.
A side can be long or short. A corner is the point where two sides meet. We can look carefully at a shape, as shown in [Figure 1], and count each side and each corner one time.
A triangle has straight sides. A square has straight sides too. If a shape has straight sides, we can touch around the outside and count: \(1\), \(2\), \(3\), and so on.
Each corner is a little turn. If a shape has \(3\) corners, it also has \(3\) angles. If a shape has \(4\) corners, it also has \(4\) angles.
Here are some shapes we can name. As [Figure 2] shows, shapes can look very different, but we can still describe them by counting sides and corners.
Circle: A circle is round. It has \(0\) straight sides and \(0\) corners.
Triangle: A triangle has \(3\) sides and \(3\) corners.
Square: A square has \(4\) sides and \(4\) corners. All \(4\) sides are the same length.
Rectangle: A rectangle has \(4\) sides and \(4\) corners. It has \(2\) long sides and \(2\) short sides. The sides across from each other match.
Pentagon: A pentagon has \(5\) sides and \(5\) corners.
The word triangle can remind us of \(3\), and pentagon can remind us of \(5\). Shape names often help us remember how many sides and corners a shape has.
When we count corners, we should move slowly around the shape so we do not count one corner twice. The same careful counting works for sides.
Some shapes have sides that are all the same length, and some shapes have sides of different lengths. In [Figure 3], one shape has matching side lengths all around, while another has long sides and short sides.
A square has \(4\) equal sides. That means each side is the same length.
A rectangle also has \(4\) sides, but not all of them have to be the same. Often it has \(2\) long sides and \(2\) short sides.
A triangle can look different from another triangle. One triangle may have sides that match, and another triangle may have one long side and two shorter sides. Even when triangles look different, they still have \(3\) sides and \(3\) corners.
Now let us look at shapes step by step. We count carefully and then name what we see.
Solved example 1
What shape has \(3\) sides and \(3\) corners?
Step 1: Count the sides.
The shape has \(3\) sides.
Step 2: Count the corners.
The shape has \(3\) corners.
Step 3: Name the shape.
A shape with \(3\) sides and \(3\) corners is a triangle.
Answer: It is a triangle.
When we know the number of sides and corners, naming many shapes becomes easier.
Solved example 2
A shape has \(4\) sides and \(4\) corners. All \(4\) sides are the same length. What shape is it?
Step 1: Count the sides and corners.
The shape has \(4\) sides and \(4\) corners.
Step 2: Look at side lengths.
All \(4\) sides are the same length.
Step 3: Name the shape.
A shape with \(4\) equal sides and \(4\) corners is a square.
Answer: It is a square.
Side length helps us tell a square and a rectangle apart. Both have \(4\) sides, but their side lengths are not described the same way.
Solved example 3
A shape has \(0\) corners and is round. What shape is it?
Step 1: Look for corners.
There are \(0\) corners.
Step 2: Notice the shape is round.
It does not have straight sides.
Step 3: Name the shape.
A round shape with \(0\) corners is a circle.
Answer: It is a circle.
We can also say that a pentagon has \(5\) sides and \(5\) corners. If we count to \(5\) all the way around, we know it is not a triangle and not a square.
Shapes are all around us every day. A wheel is like a circle. A slice-shaped sign can look like a triangle. A window may look like a rectangle. A floor tile may look like a square.
When builders make windows and doors, they use shape ideas. As [Figure 4] shows, when toy makers design blocks, they use shape ideas too. Knowing sides and corners helps us describe what we see.
A cracker might be a square, a sandwich might be cut into triangles, and a badge or little sign might be a pentagon. The same shape names from math help us talk about real things.
We can compare shapes by asking the same questions each time. How many sides? How many corners? Are the sides all the same length, or are some long and some short?
A triangle and a square are different because a triangle has \(3\) sides and \(3\) corners, while a square has \(4\) sides and \(4\) corners. We can see the side-and-corner idea clearly in [Figure 1].
A square and a rectangle are alike because both have \(4\) sides and \(4\) corners. They are different because a square has \(4\) sides of the same length, while a rectangle usually has \(2\) long sides and \(2\) short sides, as we noticed in [Figure 3].
A circle is different from all of these because it is round and has \(0\) corners. In the shape group from [Figure 2], it is the only one without straight sides.
When you look at the world, you can be a shape detective. Count the sides, count the corners, and notice the lengths of the sides. That is how we name and describe shapes.
