Question

The length of the rectangle is 15

Which statement proves that parallelogram PORT is a rectangle?

15 ^ 2 - 8 ^ 2 = T * rho ^ 2

8 + 15 = TQ

15 - 8 = TQ

8 ^ 2 + 15 ^ 2 = T * rho ^ 2

Answer 1

To prove that parallelogram PORT is a rectangle, we can use the properties of rectangles and the relationship between the sides and diagonals.

In the context of your statements, the equation that relates the sides of a rectangle to its diagonals is:

\[
a^2 + b^2 = d^2
\]

where \(a\) and \(b\) are the lengths of the sides and \(d\) is the length of the diagonal.

From the options you provided:

1. \(15^2 - 8^2 = T \cdot \rho^2\)
2. \(8 + 15 = TQ\)
3. \(15 - 8 = TQ\)
4. \(8^2 + 15^2 = T \cdot \rho^2\)

The fourth statement, \(8^2 + 15^2 = T \cdot \rho^2\), suggests a relationship involving the sides of the rectangle and reinforces the property that the sum of the squares of the sides equals the square of the diagonal. If we interpret \(T \cdot \rho^2\) as representing the square of the diagonal, this statement is consistent with proving that parallelogram PORT is a rectangle.

Therefore, the best option that proves that parallelogram PORT is a rectangle is:

**8² + 15² = T * ρ²**.