Given segment [math]AB[/math], construct each of the following: [br][list=1][*]isosceles triangle (where segment [math]AB[/math] is a leg, not the base)[/*][*]equilateral triangle [/*][*]parallelogram (with one pair of acute angles and one pair of obtuse angles)[/*][*]rectangle (with [math]AB[/math] as the longer side length)[/*][*]square [/*][/list]For each figure, once you have constructed it, drag point [math]B[/math] around. Does the figure retain it's important properties (e.g. [i]is your isosceles triangle still an isosceles triangle?[/i]). If not, try to construct that figure again so that it still fits the definition even when you move point B.
Is it possible to make a different (non-congruent) isosceles triangle using segment AB? If so, create a second isosceles triangle in the applet. If not, explain why below.
It is possible to create a second, non-congruent isosceles triangle off of segment [math]AB[/math].
How do you know that what you have constructed is an isosceles triangle?
Is it possible to make a different (non-congruent) equilateral triangle using segment AB? If so, create a second equilateral triangle in the applet. If not, explain why below.
It is [b]not[/b] possible to create a second, non-congruent equilateral triangle off of segment [math]AB[/math].
How do you know that what you have constructed is an equilateral triangle?
Is it possible to make a different (non-congruent) parallelogram using segment AB? If so, create a second parallelogram in the applet. If not, explain why below.
It is possible to create a second, non-congruent parallelogram off of segment [math]AB[/math].
How do you know that what you have constructed is a paralleogram?
Is it possible to make a different (non-congruent) rectangle using segment AB? If so, create a second rectangle in the applet. If not, explain why below.
It is possible to create a second, non-congruent rectangle off of segment [math]AB[/math].
How do you know that what you have constructed is a rectangle?
Is it possible to make a different (non-congruent) square using segment AB? If so, create a second square in the applet. If not, explain why below.
It is [b]not[/b] possible to create a second, non-congruent square off of segment [math]AB[/math].
How do you know that what you have constructed is a square?
If you have not already done so, make sure you go through all your shapes in the applets and move point [math]B[/math] around. Does your figure still meet the definition of the given shape when you do this? [br][br]If it doesn't, try a different method of construction that preserves the important characteristics of the shape when you move point [math]B[/math].
Pick one construction that retained its important characteristics even after you moved point [math]B[/math] around. Describe below (in complete sentences) how you constructed that figure.