Question

this question is a text-based essay question. write your paragraph in the space provided. your paragraph should:

• analyze whether having equal side lengths in two parallelogram - shaped parking lots guarantees that the shapes are identical.
• provide evidence/rationale from your reasoning to justify your answer.
• include correct grammar, spelling, and punctuation.

using your knowledge of geometry, explain your reasoning and justify your answer with geometric reasoning.
answer the following question.
act geometry question: by wisk

1. critical reasoning you and your friend each build two separate parking lot layouts in the shape of parallelograms. both of you use the same measurements for the four sides, making sure the lengths are exactly the same. one of you then claims that because the sides are equal, the parking lots must be identical in shape. do you agree with this? explain whether you agree or disagree, providing a counterexample to support your reasoning.

yes, because the parking lots are in the shape of a parallelogram and all sides must be equal. if they were not equal then they would not be a parallelogram. they would be a rectangle.
no, because the two shapes could be parallelograms and also be square, or trapezoid. they would be different shapes but still be parallelograms.
no, because although they are both parallelograms, they could be either a kite or a rhombus. this would make them different shapes, but still parallelograms.
no, because the shapes could be different and still be parallelograms, like a square and a rhombus which have the same length on each side.

Explanation:

A parallelogram has opposite sides equal. But for two parallelograms to be identical (congruent), not only the side - lengths but also the angles between the sides must be equal. A square (a type of parallelogram) with side - length \(s\) has all angles equal to \(90^{\circ}\), while a rhombus (another type of parallelogram) with the same side - length \(s\) can have angles other than \(90^{\circ}\). So, equal side - lengths in two parallelogram - shaped parking lots do not guarantee identical shapes.

Answer:

No, because the shapes could be different and still be parallelograms. Like a square and a rhombus which have the same length on each side.