Parallelogram Analysis: Investigating a Quadrilateral with 8 and 10 Unit Diagonals

Below is a quadrilateral:

Is it possible that it is a parallelogram?

AAABBBCCCDDDOOO108810

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1

Understand the problem

Below is a quadrilateral:

Is it possible that it is a parallelogram?

AAABBBCCCDDDOOO108810

2

Step-by-step solution

According to the properties of the parallelogram: the diagonals intersect each other.

From the data in the drawing, it follows that diagonal AC and diagonal BD are divided into two equal parts, that is, the diagonals intersect each other:

AO=OC=8 AO=OC=8

DO=OB=10 DO=OB=10

Therefore, the quadrilateral is actually a parallelogram.

3

Final Answer

Yes

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It is possible to draw a quadrilateral that is not a rectangle and that has two equal opposite sides?

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