Question

Han asked Priya to measure the angle to make sure the pieces of wood were perpendicular. Priya said, "If we were careful about the lengths of the sides of the fabric, we don't need to measure the angle. It has to be a right angle" Complete Priya's explanation to Han.

Answer 1

If the lengths of the sides of the fabric satisfy the Pythagorean theorem, then the angle between them must be a right angle.

Step-by-step explanation:

Priya is correct. If the lengths of the sides of the fabric are carefully chosen, then they can determine if the angle is a right angle without actually measuring it. This is because of a property of right triangles.

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem. So, if the lengths of the sides of the fabric satisfy this equation, then the angle between them must be a right angle.

For example, if the lengths of the sides of the fabric are 3 units and 4 units, then the length of the hypotenuse should be 5 units. This guarantees that the angle between the sides is a right angle.