Question

You know that a figure is a parallelogram. You use the distance formula to find the length of the diagonals. If they are both the same, what are the possibilities for what type of quadrilateral you have?

O trapezoid
O parallelogram
• rectangle
O rhombus

Answer 1

Answer: Rectangle (choice C)

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Step-by-step explanation:

Let's go through the possible answer choices.

• A. We can rule this out because a trapezoid is not a parallelogram. Trapezoids have exactly one pair of opposite parallel sides. The other two sides are not parallel.
• B. We rule this out because non-rectangular parallelograms will have diagonals of different lengths.
• C. This is the answer. We can prove this using SAS and then CPCTC to conclude the diagonals of any rectangle are the same length.
• D. We rule this out because the rhombus would need to be a square to have congruent diagonals. If the rhombus isn't a square, then the diagonals will be different lengths.

Footnotes:

• SAS = Side angle side
• CPCTC = corresponding parts of congruent triangles are congruent