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So if 2 opp sides are equal means it is ||gram? not matter it is square or rohbus or rectangle?
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ssruthi
So if 2 opp sides are equal means it is ||gram? not matter it is square or rohbus or rectangle?


If two opposite sides are parallel and equal, then its definitely a parallelogram. It could be a square,rhombus or rectangle ( all are types of parallelogram)
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In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(2) PQ = RS

I'm having a tough time seeing how this wouldn't be a parallelogram.

We know that a.) the figure has 4 sides and b.) that PS || PR. In addition, we are told that PQ=RS. I cannot construct a four sided figure with these constraints that doesn't have two pairs of parallel sides. Can someone please explain what I am missing and the logic behind how to solve these kinds of problems?
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In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(2) PQ = RS

I'm having a tough time seeing how this wouldn't be a parallelogram.

We know that a.) the figure has 4 sides and b.) that PS || PR. In addition, we are told that PQ=RS. I cannot construct a four sided figure with these constraints that doesn't have two pairs of parallel sides. Can someone please explain what I am missing and the logic behind how to solve these kinds of problems?

Refer to the image, where PQ=SR and PS || QR.
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Good God I don't know how I missed that. :shock:
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In statement 1 couldn't figure be a rectangle? Is a rectangle a type of parallelogram? I guess so right?

Thanks
Cheers
J :)
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In statement 1 couldn't figure be a rectangle? Is a rectangle a type of parallelogram? I guess so right?

Thanks
Cheers
J :)

Hi J,
You are Right. :)
Actually, the statement 1 could well yield
a simple parallelogram or a rectangle or a rhombus or a square.

All these are types of parallelogram:
Simple parallelogram - a quadrilateral with opposite sides equal and parallel
Rectangle - a parallelogram with adjacent sides at 90 degrees
Rhombus - a parallelogram with all sides equal
Square - a parallelogram with adjacent sides at 90 degrees and all sides equal

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(basic) properties of a parallelogram:

a) opposite sides are parallel and of the same length

b) interior angles add up to 360 degrees

c) opposite angles are equal, and adjacent angles sum to 180

Knowing the above:

1) PS=QR. Given: PS//QR. Textbook definition of //gram. sufficient.

2) PQ=RS. Does not mention whether PQ//RS, whether PS=QR, etc. insufficient.

--> A
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