# What are all the quadrilaterals that have all four sides congruent and opposite angles congruent?

Rhombus

This is the very definition of a rhombus. A square also satisfies the requirements, but a square is just a special type of rhombus.

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- Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/2 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides with lengths of #16 # and #15 #. If the parallelogram's area is #60 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram have lengths of #7 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #32 #, how long are the other two sides?
- Imagine you have a mattress, that is 160 units wide, 200 units long and 20 units thick. If you want to buy a bed sheet that fits the mattress, with a 5 unit overlap on all sides, what are the dimensions of the sheet?
- Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #56 #, how long are the other two sides?

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