Rectangle Construction Template
Below, we have a rectangle. Feel free to move any one (or more) of the points around.
Use the tools below to construct a rectangle ABCD that ALWAYS STAYS a rectangle no matter where you drag its vertices. Don't forget: You may. need to RIGHT CLICK on a point to rename it.
Construct both diagonals [math]\overline{AC}[/math] and [math]\overline{BD}[/math] of this rectangle and use the DISTANCE tool [icon]/images/ggb/toolbar/mode_distance.png[/icon] to measure their lengths. What do you notice?
In the app above, construct the intersection of both diagonals. Label this point as E (like shown in this pic.)
Now right click on both diagonals and uncheck [b]Show Object[/b] (to hide them). Then use the SEGMENT tool [icon]/images/ggb/toolbar/mode_segment.png[/icon]to construct segments [math]\overline{AE}[/math], [math]\overline{BE}[/math], [math]\overline{CE}[/math], and [math]\overline{DE}[/math]. What do you notice?
Use the POLYGON [icon]/images/ggb/toolbar/mode_polygon.png[/icon] tool to construct triangle [i]AEB, CEB, DEC, [/i]and [i]AED[/i]. Then use the ANGLE [icon]/images/ggb/toolbar/mode_angle.png[/icon] tool to measure the angles of each of these polygons. What do you notice?
In the picture (with graph paper background) above, which angles are congruent to angle 1?
In the picture (with graph paper background) above, which angles are congruent to angle 2?
What properties here hold true for [b]ALL RECTANGLES[/b]?
What properties here hold true for [b]RECTANGLES ONLY[/b] and are not necessarily true for all parallelograms?