**Narration**
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Welcome to this tutorial on **Properties of Quadrilaterals **in **GeoGebra.**
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In this tutorial we will learn,
To construct quadrilaterals and understand the properties of quadrilaterals using **GeoGebra**.

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Here I am using:
**Ubuntu Linux OS**, version 14.04

**GeoGebra **version 5.0.438.0-d

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To follow this tutorial, learner should be familiar with **GeoGebra** interface.
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If not for relevant **GeoGebra **tutorials, please visit our website.
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Let us begin our demonstration.
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I have already opened the **GeoGebra **interface.
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For this tutorial, I will first uncheck the **Axes**.
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To do that, right-click on **Graphics view**.
The **Graphics** menu opens.

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Click on the **Axes** check-box.
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I will increase the font size for better view.
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Go to **Options** menu, navigate to **Font Size**.
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From the sub-menu, select **18 pt** radio button.
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Now let us construct a parallelogram.
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Click on the **Segment with Given Length** tool.
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Click on the ** Graphics view**.
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The **Segment with Given Length** text box opens.
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In the **Length field**, type 5 and click on **OK** button.
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Segment **AB** with length 5 cm and labelled as **f**, is drawn.
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Let us delete the point that was drawn mistakenly.
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This point may not be required for the actual drawing.
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Right-click on the point. From the sub-menu, select the **Delete **option.
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Next click on the **Parallel Line** tool.
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Click below line **AB** to draw point **C **then click on line **AB**.
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A parallel line to segment **AB** passing through **C**, is drawn.
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Using **Segment** tool, join the points **A** and **C**.
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Click again on **Parallel Line** tool, click on segment **AC** and then click on point **B**.
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Two parallel lines **g** and **i** intersect at a point.
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Click on **Intersect** tool and click on the point of intersection as **D**.
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Now using the **Segment** tool, join the points, **C**, **D** and **D**, **B**.
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Parallelogram** ABDC** is now complete.
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We will hide the lines **g** and **i**, so that we can see the parallelogram clearly.
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Right-click on line **g**, from the submenu click on **Show Object** check-box.
Similarly I will hide the line **i**.

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Now we will explore the properties of parallelogram **ABDC**.
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From the **Algebra view**, we can find that,
segments **f** and **j** are equal and segments **h** and **k **are equal.

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Observe that, the opposite sides are parallel and equal.
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Let us now measure the angles of the parallelogram.
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Click on **Angle** tool.
Click on the points **D C A**

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**C A B**
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**A B D**
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**B D C**.
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Observe that the opposite angles are equal.
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Now we will convert the parallelogram **ABDC** to a rectangle.
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Click on **Move** tool.
Click and drag point **C** until you see 90 degrees angle.

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Drag the labels to see them clearly.
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Observe that all the angles changed to 90 degrees.
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Now let us learn to construct a kite.
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For this I will open a new **GeoGebra** window.
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Click on **File** and select **New Window**.
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To contruct a kite, we will draw two circles that intersect at two points.
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Click on **Circle with Centre through point** tool.
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Then click on **Graphics view.**
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Point** A** is drawn, this is the centre of the circle.
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Click again at some distance from point **A**.
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Point **B** appears.
This completes the circle **c**.

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Similarly, we will draw another circle with centre **C** and passing through **D**.
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Notice that the two circles **c** and **d** intersect at two points.
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Click on **Intersect** tool and click on the circles **c** and **d**.
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**E** and **F** are the intersection points of the circles.
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Now let us draw the required quadrilateral using these circles.
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Click on **Polygon** tool.
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Click on the points **A, E, C, F **and **A** again to complete the quadrilateral.
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Notice in the **Algebra View** that two pairs of adjacent sides are equal.
The drawn quadrilateral is a kite.

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Pause the tutorial and do this assignment.
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Measure the angles of the kite and check what happens.
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Draw diagonals and locate the intersection point of the diagonals.
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Measure the angle at the intersection of the diagonals.
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Check if diagonals bisect each other.
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Your completed assignment should look like this.
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To delete all the objects, press **Ctrl** + **A** and then press **Delete** key on the Key board.
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Now let us construct a rhombus.
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Click on **Segment with Given Length **tool.
Click on the **Graphics view.**

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**Segment with Given Length** text box opens.
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In the **Length **field, type 4 and click on **OK **button.
A segment with 4 units is drawn.

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Let us construct a circle with center **A** and passing through **B**.
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Click on **Circle with Centre through Point** tool.
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Click on points **A** and **B** to complete the circle.
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Using **Point** tool, mark a point **C** on the circumference of the circle.
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Click on **Segment** tool and then click on points **A** and **C**.
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This will join the points **A** and **C.**
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Click on the **Parallel line** tool and click on the line **AB** and then on point **C**.
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We see a line parallel to **AB** passing through **C**.
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Similarly, draw a parallel line to segment **AC ** passing through **B**.
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Notice that the lines **i** and **h** intersect at a point.
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Using **Intersect** tool, we will mark the point of intersection as **D**.
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Using the **Segment** tool, join the points **A**, **D** and **B**, **C**.
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A quadrilateral **ABDC** with diagonals **AD** and **BC** is drawn.
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The diagonals intersect at a point.
Using **Intersect** tool, mark the point of intersection as **E**.

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Pause the tutorial and do this assignment.
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Check if the diagonals of the quadrilateral **ABDC **bisect each other.
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Also check if the diagonals are perpendicular bisectors.
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Your completed assignment should look like this.
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Now let us construct a cyclic quadrilateral.
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For this, let us open **Graphics 2 view**.
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Go to **View** menu and select **Graphics 2** check box.
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**Graphics 2 view** window opens, next to existing **Graphics view**.
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Drag the border of the existing **Graphics view**, to see **Graphics 2 view**.
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Now select **Regular Polygon** tool.
Click twice on **Graphics 2 view**.

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The **Regular Polygon** text box opens with default value 4.
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Click on the **OK **button.
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A square **FGHI** is drawn in **Graphics 2 view**.
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Let's construct perpendicular bisectors to segments **FG** and **GH**.
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Select the **Perpendicular Bisector** tool from the tool bar.
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Click on the points **F**, **G**and **G**, **H**.
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Observe that the perpendicular bisectors intersect at a point.
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Using **Intersect **tool we will mark this point as **J**.
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Now, Let's construct a circle with centre as **J** and passing through **F**.
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Click on the **Circle with center through Point **tool, click on point **J**.
Then click on point **F**.

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A cyclic quadrilateral **FGHI **is drawn.
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Now we will display its area.
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From the **Angle** tool drop down, click on the **Area** tool.
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Then click on the quadrilateral **FGHI **to display its area.
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As an assignment,
Draw a trapezium

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Measure its perimeter and area.
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Your completed assignment should look like this.
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Let us summarise what we have learnt.
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In this tutorial we have learnt, To construct quadrilaterals and understand the properties of quadrilaterals using **GeoGebra.**
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The video at the following link summarises the Spoken Tutorial project.
Please download and watch it.

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The **Spoken Tutorial Project **team conducts workshops using spoken tutorials and gives certificates.
For more details, please write to us.

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Please post your questions in this forum.
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Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
More information on this mission is available at this link.

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This is Madhuri Ganapathi from, IIT Bombay signing off.
Thank you for watching.