Question

pythagorean unit practice
parallelogram pqrt is shown.
which statement proves that parallelogram pqrt is a rectangle?
a 15 - 8 = tq
b 8² + 15² = tq²
c 8 + 15 = tq
d 15² - 8² = tq²

Explanation:

Step1: Recall rectangle - property

In a rectangle, the diagonals and the sides form right - triangles. For right - triangle $\triangle TQR$, if $\angle R = 90^{\circ}$ (a condition for the parallelogram to be a rectangle), by the Pythagorean theorem, in a right - triangle with legs of lengths $a$ and $b$ and hypotenuse of length $c$, we have $a^{2}+b^{2}=c^{2}$. Here, $a = 8$, $b = 15$, and the hypotenuse is the diagonal $TQ$.

Step2: Apply Pythagorean theorem

So, $8^{2}+15^{2}=TQ^{2}$.

Answer:

B. $8^{2}+15^{2}=TQ^{2}$