Geometry > Drawing Quadrilaterals

Square | Types of Quadrilaterals  | Concave - Complex Quadrilateral

Drawing Quadrilaterals

Square

Press Apps key and select Geometry. Press the soft key Reset. Press Geometry again or soft key Start to begin.

The app comes up in the Plot View, the Geometry app’s drawing view. Use Cmds > 1 Zoom > 1 In.

Press the Symb key to switch to the Symbolic View. The Geometry Symbolic View allows editable definitions of objects drawn in the Geometry Plot View.  Select Cmds > 1 Point > 1 Point. Key in -3,3 and press soft key OK or the Enter key. Repeat the process to key in the next three points using the values shown in the Geometry Symbolic View screen.

Remark: The definition of the points A, B, C, and D add a G. The variable for the points are referenced as GA, GB, GC, and GD. To enter a new definition move to the blank line.

For the quadrilateral definition use Cmds > 3 Polygon > 4 Quadrilateral. Use the soft key Vars to enter GA, GB, GC, and GD. Separate the points in the quadrilateral definition by using a comma.

Press the Num key to switch to the Geometry Numeric View. Select Cmds > 3 Tests > 8 Parallelogram. Use the soft key Vars to select the quadrilateral GE. Check the definition's display box so that it will show on the Geometry Plot View screen. The number 4 signifies that the parallelogram is a square.

Press the Plot key to see the results.

 

dq_sq1_calc

dq_sq2_calc

dq_sq_calc


Types of Quadrilaterals

Right Trapezoid

In the Geometry Symbolic View select definition for GA. Use the soft key Edit to change GA value to -5,3. Press the Plot key to see the results. We now have a right trapezoid. A right trapezoid is a quadrilateral with only one pair of parallel sides and two right angles. The number 0 signifies that the quadrilateral is not a parallelogram/

Isosceles Trapezoid

Next, in the Geometry Symbolic View select definition for GB. Use the soft key Edit to change GB value to 5,3. Press the Plot key to see the results. We now have a isosceles trapezoid. An isosceles trapezoid is a quadrilateral with only one pair of parallel sides in which the base angles are equal and therefore the left and right side lengths are also equal. Again, the number 0 signifies that the quadrilateral is not a parallelogram.

Remark: A convex quadrilateral with only one pair of parallel sides is referred to as a trapezoid. Moving point C one to the right would be an example of a convex quadrilateral with only one pair of parallel sides and no special trait such as right or isosceles.

Rectangle

In the Geometry Symbolic View select definition for GC. Use the soft key Edit to change GC value to 5,-3. Next, change the definition for GD to -5,-3. Press the Plot key to see the results. We now have a rectangle. The number 3 signifies that the parallelogram is a rectangle.

Parallelogram

Use the Geometry Symbolic View editing process to set GA, GB, GC, and GD definitions to the values shown in the fourth illustration. Press the Plot key to see the results. The number 1 signifies that the quadrilateral is only a parallelogram.  A parallelogram is a quadrilateral with opposite sides parallel.

Rhombus

Switch GA, GB, GC, and GD definitions back to our original square values by using the soft key Edit on their current values.

To show how our original square is related to a rhombus we add segments GH and GI; rotate them, GG and GJ; and then add the definition for a rhombus, GL. This is shown in the Geometry Symbolic View screen on the right.

The definition of a rhombus covers the rotated segments, GG and GJ. Notice in the Plot View, last drawing on the right, that the ends of rotated segments and top vertices of the rhombus are not labeled,

Use soft key Cmds menu and soft jey Vars menu to add the definitions to the Geometry Symbolic View. Press the Plot key to see the results.

g1_dq_trap1_calc

g1_dq_trap2_calc

g1_dq_rect_calc

g1_dq_pg_calc

g1_dq_rhombus1_calc

g1_dq_rhombus2_calc

 


Concave - Complex Quadrilaterals

We will use the Plot View to draw our concave quadrilateral and complex quadrilateral.

Concave Quadrilateral

Clear the Plot View variables by pressing the Clear key. To the “Clear all variables?” dialog box press the soft key OK or Enter key. Use Cmds > 1 Zoom > 1 In.

See the first illustration on the right of a concave quadrilateral. Select Cmds > 4 Polygon > 4 Quadrilateral.  We are prompted to select a point. Move to a location in Quadrant II and press Enter. To the select another point prompt move to a point in Quadrant III. At this point we will see a line segment from our first point. Press Enter. To the select another point prompt move to a point in Quadrant IV. We now see a triangle. Press Enter. To the select another point prompt move back to a point in Quadrant III below and to the left of our earlier point in this quadrant.. At this point we will see a concave quadrilateral. Press Enter. Labels are added to the vertices of our quadrilateral.

Press the Num key to switch to the Geometry Numeric View, screen 2. Select Cmds > 3 Tests > 8 Parallelogram. Check the definition's display box so that it will show on the Geometry Plot View screen. The number 0 signifies that the quadrilateral is not a parallelogram.

Press the Symb key. We can now use the Geometry Symbolic View editing process to set GA, GB, GC, and GD definitions to specific values, screen 3. Press the Plot key to see the changes, screen 1.

Remark: Plot View was all that was needed for investigating concave quadrilaterals. Our Geometry Symbolic View screen edited the Plot View point values to provide a cleaner representation for documentation purposes.

Complex Quadrilateral

Use Clear to clear out previous work..To the “Clear all variables?” dialog box press the soft key OK or Enter key. Use Cmds > 1 Zoom > 1 In.

Repeat the above process with the order of point selection being Quadrant II, Quadrant I, Quadrant III, and Quadrant IV. Screen 4 shows the results using an  A of -3,3; B of 4,4; C of -3,-1; and D of 3,-2.

Selecting point A, B, C, or D and moving it is an easy way to experiment with our drawing. There are two ways to do this:

Method 1: In the Geometry Symbolic View select the GB definition. Screen 3 from the concave quadrilateral illustrates the GB definition selected. Press the Plot key. We would then grab point B and move it. This allows us to experiment with point B‘s location and visually see how the location affects the drawing.

Method 2: This is the preferred method. From the Plot View touch or select a point near point B, screen 5. The cross hair location is X:3.85 Y:4.05, a value near point B. The definitions labels for the point and quadrilateral, B, E  show up in the lower right hand corner. Press Enter. We would then grab the point B and move it. This allows us to experiment with the point B‘s location and visually see how the location affects the drawing.

g1_dq_concave_calc

g1_dq_concave2_calc

g1_dq_concave1_calc

g1_dq_complex1_calc

g1_dq_complex_pt_calc

 
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