Question

the figure is a parallelogram. one diagonal measures 28 units.
is the figure a rectangle? explain
yes, it is a rectangle
because the
diagonals are
congruent.
no, it is not a
rectangle because
the sides of the
parallelogram do not
meet at right angles.
yes, it is a rectangle
because the sides of
the parallelogram do
meet at right angles.
no, it is not a
rectangle because
the diagonals are
congruent.

Explanation:

Step1: Check the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Here, \(a = 20\), \(b=21\), and \(c = 28\).
Calculate \(a^{2}+b^{2}\): \(20^{2}+21^{2}=400 + 441=841\).
Calculate \(c^{2}\): \(28^{2}=784\).
Since \(20^{2}+21^{2}
eq28^{2}\), the sides of the parallelogram do not meet at right - angles.

Step2: Recall the property of a rectangle

A rectangle is a parallelogram with four right - angles.

Answer:

No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.