Final answer:
Parallelogram RSTW is a rectangle because it has one right angle.
Step-by-step explanation:
To determine if parallelogram RSTW is a rectangle, we need to examine its properties. One of the properties of a rectangle is that all angles are right angles. In a parallelogram, opposite angles are congruent, but not necessarily right angles. So, we need to find the measure of one angle to determine if it is a right angle.
Using the Pythagorean theorem, we can find the measure of angle RST. Let's use c as the hypotenuse and a and b as the legs of the right triangle formed by RS, ST, and RT. We know that RS = 7, ST = 24, and RT = 25.
c^2 = a^2 + b^2
Plugging in the values, we get:
25^2 = 7^2 + 24^2
Simplifying, we have:
625 = 49 + 576
625 = 625
Since the equation is true, it means that angle RST is a right angle. Therefore, parallelogram RSTW is a rectangle because it has one right angle.