Question

analyzing sides and diagonals of a parallelogram
claire is designing a banner that will hang in her classroom. the length of one diagonal of the banner is 48 inches, and the sides are 25 inches long. is the banner a square?
it is not a square because opposite angles are not congruent.
it is not a square because the angles at the vertices are not right angles.
it is a square because all the sides are congruent.
it is a square because the diagonals are perpendicular.

Explanation:

Step1: Recall properties of a square

In a square, if side length is $a$ and diagonal length is $d$, by Pythagorean theorem $d^{2}=2a^{2}$. Here $a = 25$ inches and $d=48$ inches.

Step2: Check Pythagorean - relation

Calculate $2a^{2}=2\times25^{2}=2\times625 = 1250$, and $d^{2}=48^{2}=2304$. Since $d^{2}
eq2a^{2}$, the angles at the vertices are not right - angles. A square has right - angled vertices.

Answer:

It is not a square because the angles at the vertices are not right angles.