SOLUTION: Sketch two noncongruent parallelograms ABCD and EFGH such that line AC is congruent to line BD, line BD is congruent to line EG and line EG is congruent to line FH. (I tried to dra

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Question 984387: Sketch two noncongruent parallelograms ABCD and EFGH such that line AC is congruent to line BD, line BD is congruent to line EG and line EG is congruent to line FH. (I tried to draw a rectangle and a trapezoid but couldn't make these lines congruent. The lines that these question are referring to are diagonals. How can this be drawn? If the answer can't be drawn please describe the sketch. Thank you :)
Found 3 solutions by solver91311, katewalk11740, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Cannot be done. AC congruent to BD means ABCD is not only a parallelogram, but it is also a rectangle. EG congruent to FH means EFGH is also a rectangle. And BD congruent to EG means that both rectangles are congruent.

John

My calculator said it, I believe it, that settles it

Answer by katewalk11740(1)   (Show Source): You can put this solution on YOUR website!
The question does not specify what type of parallelogram you should draw, only that they 1) not be congruent and 2) have diagonals, that are all congruent to each other.
First, decide on a length of diagonal, say 4 cm. Draw this. Find the midpoint and draw a second diagonal also 4 cm long through the midpoint of the first. Then connect the outside endpoints and you have your first parallelogram.
Next, draw a 4 cm line and again find its midpoint. Now, using a different angle from the first parallelogram, make this diagonal so the two cross in a narrow fashion. When you connect the endpoints you will have a second narrow parallelogram.
The diagonals are all congruent, but the parallelograms are not congruent.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Sketch two noncongruent parallelograms ABCD and EFGH such that line AC is congruent to line BD,
line BD is congruent to line EG and line EG is congruent to line FH.
(I tried to draw a rectangle and a trapezoid but couldn't make these lines congruent.
The lines that these question are referring to are diagonals. How can this be drawn?
If the answer can't be drawn please describe the sketch. Thank you :)
~~~~~~~~~~~~~~~~ 

They tell you about parallelograms that have congruent diagonals.

HENCE, these parallelograms are RECTANGLES (only rectangles, among all parallelograms, have congruent diagonals !)



Next, to make a sketch, draw a circle, first.


Incribe any rectangle in this circle.  Call this rectangle ABCD.


Next, inscribe any other non-congruent rectangle in this circle.  Call the second parallelogram as EFGH.


These parallelograms have CONGRUENT DIAGONALS, but are not congruent rectangles.


They give the solution to your problem.


Why the diagonals of these rectangles are congruent ? - - - Due to this simple reason, that a diagonal of any rectangle,

inscribed in a circle, is the circle's diameter, and all diameters of any circle are congruent (!)

Hope this helps.

---------------

On the way, you learned from me a new for you FACT, that a diagonal of a rectangle,
inscribed in a circle, is a circle diameter.




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