# On a blueprint for a house, if the master bedroom is a parallelogram with at least one right angle, then will the master bedroom will be the shape of a rectangle, a rhombus, a square or just a parallelogram?

Rectangle (or even square)

A parallelogram has opposite angles equal and adjacent angles supplementary.

If one angle is right, then its opposite is also right. Since the angle is supplementary to its adjacents, it follows that its adjacents are also right. Hence, if one angle of a parallelogram is right, then all its angles are right and we have a rectangle.

Is the master bedroom a square? Not necessarily. Equal angles does guarantee that the sides of the parallelogram are also equal.

Is the master bedroom a rhombus? Only if it is a square.

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If the master bedroom on a blueprint for a house is a parallelogram with at least one right angle, then the master bedroom will be the shape of a rectangle.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #5 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #pi/3 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #48 #, how long are the other two sides?
- Given MPRK is a parallelogram, how would you prove, in two-column format, that the measure of angle MTK = measure of angle PMT + measure of angle RKT?
- Two rhombuses have sides with lengths of #12 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?
- Two opposite sides of a parallelogram each have a length of #16 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #64 #, how long are the other two sides?

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