Cut a piece of paper to form a triangle shape. Tear off the three corners of the triangle. Then put the three corners together. Describe what you see. What mathematical truth does this activity illustrate? Explain
When you cut a piece of paper to form a triangle shape and tear off the three corners, you will be left with three triangular corners. If you put these three corners together, you will notice that they form a straight line or, more precisely, a straight angle.
This activity illustrates the mathematical truth known as the Angle Sum Property of a Triangle. According to this property, the sum of the interior angles of a triangle is always equal to 180 degrees.
To understand how this property applies to the activity, let's consider the original triangle shape. A triangle has three interior angles, and when you tear off the corners of the triangle, you are removing those angles from the original triangle. The three interior angles of the triangle, when put together, form a straight line, which is equivalent to a 180-degree angle.
In other words, by tearing off the corners of the triangle and assembling them, you are essentially verifying the Angle Sum Property of a Triangle, which states that the sum of the angles in any triangle is always equal to 180 degrees.