1. Feb 17, 2012

### luke8ball

Hi Guys! I've attached a picture of the setup if you don't have Geometer's Sketchpad software. I honestly have no idea where to begin with this problem, as I've been staring at it for hours. Nevertheless, I've still put some thoughts down on what I think I should do.

1. The problem statement, all variables and given/known data

Use Geometer’s Sketchpad and draw points A, B, C (not all three are collinear).
Construct segments AC and BC.
Draw circle with center A and radius AC
Draw circle with Center B and radius BC
Label the other intersection of the circles D.

a. Drag point A, B, C, or D to change the shape of ABCD. What types of quadrilaterals can be formed? Explain.

b. Are there types of quadrilaterals that cannot be formed? List and explain.

3. The attempt at a solution

Square – Yes. If the two circles have radii of the same length, and if you adjust points C and D accordingly, you can have all 90° angles.

Rectangle – You can have a rectangle with all equal sides, but you can’t have a rectangle that isn’t a square, as the adjacent sides are always radii of the same circle, and cannot be different lengths.

Rhombus – You can have a rhombus because you can have a square, and you could just adjust the angles if you wanted a rhombus that wasn’t a square?

Parallelogram – You can have a parallelogram, but it has to be a rhombus as well, because adjacent sides must be equal.

Kite – You can certainly have a kite, as the pairs of adjacent sides (radii) will always be equal.

Any hints would be truly appreciated; I feel like an idiot staring at this problem in Geometer's Sketchpad.

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2. Feb 17, 2012

### Some Pig

You can't create quadrilaterals that have 3 unequal sides or its sides crossed.

3. Feb 17, 2012

### luke8ball

Thanks for the response!

So out of the list I've given, there are any of those that specifically can't be formed?
Does this also imply that a trapezoid must be an isosceles trapezoid?

4. Feb 17, 2012

### Some Pig

The only trapezium can be formed is a square.