Rectangle Construction Template (V2)
Below, we have a rectangle. Feel free to move any one (or more) of the points around.
STUDENTS: Complete the following in the GeoGebra app below.
[list=1][*]Construct a [b]SEGMENT [/b][icon]/images/ggb/toolbar/mode_segment.png[/icon] with endpoints [i]A[/i] and [i]B[/i]. [/*][*]Use the [b]PERPENDICULAR LINE [/b]tool [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon] to construct a line perpendicular to the segment you drew in step 1 that passes through [i]A[/i]. To do this, select the tool [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon], select the segment itself, and then click on point [i]A[/i]. [/*][*]Now construct a line through [i]B[/i] that is perpendicular to the segment you constructed in step 1. [/*][*]Use the [b]POINT ON OBJECT[/b] tool [icon]/images/ggb/toolbar/mode_pointonobject.png[/icon] to plot a point [i]C[/i] on the perpendicular line you constructed in step 3. [/*][/list][br][size=200][b]5. Now.....[/b][br]Construct a point [i]D [/i]so that quadrilateral [i]ABCD[/i] is a [b]rectangle[/b]. [br][/size]
6. After constructing your rectangle, right click on the lines and hide them all. Then use the POLYGON tool to construct rectangle ABCD.
7. Use the [b]DISTANCE[/b] tool [icon]/images/ggb/toolbar/mode_distance.png[/icon] to measure the four sides of this rectangle. [br]8. Use the [b]ANGLE [/b]tool [icon]/images/ggb/toolbar/mode_angle.png[/icon] to measure the four interior angles of this rectangle. [br](Of course, they better all come out to be 90 degrees.) [br][br]
9. 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.)
10. 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?
11.
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?
12.
In the picture (with graph paper background) above, which angles are congruent to angle 1?
13.
In the picture (with graph paper background) above, which angles are congruent to angle 2?
14. What properties here hold true for [b]ALL RECTANGLES[/b]?
15. What properties here hold true for [b]RECTANGLES ONLY[/b] and are not necessarily true for all parallelograms?