Parallelograms - 4

REMEMBER: You can always click on (top right) to undo your last action.

1. Generate side lengths and height.

• Click on the **New Dimensions** button (and wait 2 secs).

2. Make the base of your parallelogram.

• Click on "Segment with** given length from point**" icon.

• Then click on the point A (it will glow) and In the box type the number of the base of your parallelogram. Hit Enter.

• Make this line blue, thick 4 and show its value - that is, right-click on the line, click on Properties and change the color to blue and the line thickness to 4 select "Show Label" and then click on the next to Name and select Value. Hit Enter.

We must make the side and height together!

3. First steps

• Click on "Line through 2 points" icon and then click on A and then on B.

• Click on "Circle with **center and radius**" icon. Click on **B** and then type in the value of the** side ** of your parallelogram.

! Every point on this circle can be a side point -

we need to find the point at the correct height !

4. Second steps

• Click on "Point" icon. Click anywhere on line AB within the circle. The point C will be drawn on the line.

• Click on "Perpendicular line" and then click on C and then on the line AB.

• Right-click on the perpendicular and deselect "Show object".

• Click on "Segment through 2 points" icon and then click on C and then on E. Make this line dark red, thick **4**, **dashed** and show its **value** - it must show its value!

This line is the height of the parallelogram!

5. Third steps

• Click on . Click on B and then D. Make this line red, thick 4, and show its **value**.

6. Draw the other 2 sides of the parallelogram.

• Click on "Parallel line" icon.

• Click on point E, then on line AB (to get top).

• Click on point A, then on line AE (to get leftt side).

7. Find the 4th vertex of the parallelogram. It is the intersection of the two lines we have just drawn.

top lineright side.

8. Close your parallelogram AFEB.

• Click on . Click on A and then F. Click on F and then E.

9. Clean up

10. Play with your parallelogram.

• Click and drag the blue point A ( moves the parallelogram) or, blue point B (rotates the parallelogram).

Notice that the **angles **never change since they are completely defined by the length of the two adjacent sides and the height.

This is a good GeoGebra construction - unlike the previous one! The reason is that by placing C on the line AB instead of on the circle, the height will not change. This is as it should be since it is one of our original dimensions.

• Click on **Reset** to start over.

LFS, Stabie construction by Robert Fant! - Created with GeoGebra