the figure is a parallelogram. one diagonal measures 28 units. is the figure a rectangle? explain. no, it is…

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

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

Answer

Explanation:

Step1: Recall rectangle properties

A rectangle is a parallelogram with four - right angles. Also, the diagonals of a rectangle are congruent. Just because the diagonals of a parallelogram are congruent does not necessarily mean it is a rectangle. We need to check if the sides meet at right - angles.

Step2: Apply Pythagorean theorem

For a right - triangle, if the sides of a triangle formed by two adjacent sides and a diagonal of the parallelogram satisfy (a^{2}+b^{2}=c^{2}), then the angle between the two adjacent sides is a right - angle. Consider the triangle with sides 20, 21 and 28. Calculate (20^{2}+21^{2}=400 + 441=841) and (28^{2}=784). Since (20^{2}+21^{2}\neq28^{2}), the sides of the parallelogram do not meet at right - angles.

Answer:

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