Welcome to this tutorial on Properties of Quadrilaterals in GeoGebra.
In this tutorial we will learn, To construct quadrilaterals and understand the properties of quadrilaterals using GeoGebra.
Here I am using: Ubuntu Linux OS, version 14.04 GeoGebra version 5.0.438.0-d
To follow this tutorial, learner should be familiar with GeoGebra interface.
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Let us begin our demonstration.
I have already opened the GeoGebra interface.
For this tutorial, I will first uncheck the Axes.
To do that, right-click on Graphics view. The Graphics menu opens.
Click on the Axes check-box.
I will increase the font size for better view.
Go to Options menu, navigate to Font Size.
From the sub-menu, select 18 pt radio button.
Now let us construct a parallelogram.
Click on the Segment with Given Length tool.
Click on the Graphics view.
The Segment with Given Length text box opens.
In the Length field, type 5 and click on OK button.
Segment AB with length 5 cm and labelled as f, is drawn.
Let us delete the point that was drawn mistakenly.
This point may not be required for the actual drawing.
Right-click on the point. From the sub-menu, select the Delete option.
Next click on the Parallel Line tool.
Click below line AB to draw point C then click on line AB.
A parallel line to segment AB passing through C, is drawn.
Using Segment tool, join the points A and C.
Click again on Parallel Line tool, click on segment AC and then click on point B.
Two parallel lines g and i intersect at a point.
Click on Intersect tool and click on the point of intersection as D.
Now using the Segment tool, join the points, C, D and D, B.
Parallelogram ABDC is now complete.
We will hide the lines g and i, so that we can see the parallelogram clearly.
Right-click on line g, from the submenu click on Show Object check-box. Similarly I will hide the line i.
Now we will explore the properties of parallelogram ABDC.
From the Algebra view, we can find that, segments f and j are equal and segments h and k are equal.
Observe that, the opposite sides are parallel and equal.
Let us now measure the angles of the parallelogram.
Click on Angle tool. Click on the points D C A
C A B
A B D
B D C.
Observe that the opposite angles are equal.
Now we will convert the parallelogram ABDC to a rectangle.
Click on Move tool. Click and drag point C until you see 90 degrees angle.
Drag the labels to see them clearly.
Observe that all the angles changed to 90 degrees.
Now let us learn to construct a kite.
For this I will open a new GeoGebra window.
Click on File and select New Window.
To contruct a kite, we will draw two circles that intersect at two points.
Click on Circle with Centre through point tool.
Then click on Graphics view.
Point A is drawn, this is the centre of the circle.
Click again at some distance from point A.
Point B appears. This completes the circle c.
Similarly, we will draw another circle with centre C and passing through D.
Notice that the two circles c and d intersect at two points.
Click on Intersect tool and click on the circles c and d.
E and F are the intersection points of the circles.
Now let us draw the required quadrilateral using these circles.
Click on Polygon tool.
Click on the points A, E, C, F and A again to complete the quadrilateral.
Notice in the Algebra View that two pairs of adjacent sides are equal. The drawn quadrilateral is a kite.
Pause the tutorial and do this assignment.
Measure the angles of the kite and check what happens.
Draw diagonals and locate the intersection point of the diagonals.
Measure the angle at the intersection of the diagonals.
Check if diagonals bisect each other.
Your completed assignment should look like this.
To delete all the objects, press Ctrl + A and then press Delete key on the Key board.
Now let us construct a rhombus.
Click on Segment with Given Length tool. Click on the Graphics view.
Segment with Given Length text box opens.
In the Length field, type 4 and click on OK button. A segment with 4 units is drawn.
Let us construct a circle with center A and passing through B.
Click on Circle with Centre through Point tool.
Click on points A and B to complete the circle.
Using Point tool, mark a point C on the circumference of the circle.
Click on Segment tool and then click on points A and C.
This will join the points A and C.
Click on the Parallel line tool and click on the line AB and then on point C.
We see a line parallel to AB passing through C.
Similarly, draw a parallel line to segment AC passing through B.
Notice that the lines i and h intersect at a point.
Using Intersect tool, we will mark the point of intersection as D.
Using the Segment tool, join the points A, D and B, C.
A quadrilateral ABDC with diagonals AD and BC is drawn.
The diagonals intersect at a point. Using Intersect tool, mark the point of intersection as E.
Pause the tutorial and do this assignment.
Check if the diagonals of the quadrilateral ABDC bisect each other.
Also check if the diagonals are perpendicular bisectors.
Your completed assignment should look like this.
Now let us construct a cyclic quadrilateral.
For this, let us open Graphics 2 view.
Go to View menu and select Graphics 2 check box.
Graphics 2 view window opens, next to existing Graphics view.
Drag the border of the existing Graphics view, to see Graphics 2 view.
Now select Regular Polygon tool. Click twice on Graphics 2 view.
The Regular Polygon text box opens with default value 4.
Click on the OK button.
A square FGHI is drawn in Graphics 2 view.
Let's construct perpendicular bisectors to segments FG and GH.
Select the Perpendicular Bisector tool from the tool bar.
Click on the points F, Gand G, H.
Observe that the perpendicular bisectors intersect at a point.
Using Intersect tool we will mark this point as J.
Now, Let's construct a circle with centre as J and passing through F.
Click on the Circle with center through Point tool, click on point J. Then click on point F.
A cyclic quadrilateral FGHI is drawn.
Now we will display its area.
From the Angle tool drop down, click on the Area tool.
Then click on the quadrilateral FGHI to display its area.
As an assignment, Draw a trapezium
Measure its perimeter and area.
Your completed assignment should look like this.
Let us summarise what we have learnt.
In this tutorial we have learnt, To construct quadrilaterals and understand the properties of quadrilaterals using GeoGebra.
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