This lesson is #9 of 34 in One Mathematical Cat, Please! Topics in Geometry

On this worksheet, you are only given hints to various GeoGebra constructions. You will need to figure out how to do many things yourself!

This worksheet assumes you have the level of knowledge and experience with GeoGebra that is provided in:
GeoGebra Tutorial: Introduction to GeoGebra
GeoGebra Worksheet: Triangles
GeoGebra Tutorial: GeoGebra Basics

GeoGebra Worksheet: QUADRILATERALS

1. You may need to complete this worksheet at several different sittings. Be sure to save your GeoGebra file at each stage (File-Save) and then re-open it (File-Open) as needed.
2. When you are asked to construct (say) an arbitrary rectangle, this means the following:
   -- no matter how you move points/segments, the object remains a rectangle; and
   -- you can obtain any desired rectangle by appropriately moving points/segments
3. Select   Options-Labeling-No new objects   to turn off automatic labeling.
4. Construct an arbitrary quadrilateral, as follows:
   -- With the POLYGON tool, create a quadrilateral.
   (Hint: lay out the points in a counter-clockwise direction; otherwise, you might not immediately get the angles you want in the next step!)
   -- With the ANGLE tool, click on the polygon to obtain all the interior angles.
   -- In the INPUT FIELD (down the bottom), find the sum of these interior angles. (Hint: Use the GREEK LETTER MENU to get your angles.)
   -- Use dynamic text to get the result shown below, with exactly the same formatting as shown:
   
   
   -- Make sure that the $\,360^{\circ}\,$ is not static text! This sum must be computed by GeoGebra.
5. Construct an arbitrary RECTANGLE:
   -- There are many ways to do this; one approach is given here.
   -- With the SEGMENT tool, construct your first side.
   -- With the ANGLE WITH GIVEN SIZE tool, create a $\,90^{\circ}\,$ angle.
   -- Using the point at $\,90^{\circ}\,$ that was just created, draw a line that is perpendicular to your first side, as shown below.
   -- Put a point on this line, by clicking on it with the POINT tool active.
   -- This point can move freely along the line, but is not allowed to move off the line.
   
   
   
   -- Using the free point on the line, construct the second side of the rectangle with the SEGMENT tool.
   -- Be sure to hide all auxiliary objects.
   -- Finish the rectangle; the PARALLEL LINE and INTERSECTION tools may be helpful!
   -- Label all the angles, and construct the dynamic text as shown below:
   
   
6. Construct an arbitrary RHOMBUS:
   -- Use the SLIDER tool to create a slider named ‘side’ with values from $\,0\,$ to $\,10\,$ and increment $\,0.1\,.$
   -- Use the SEGMENT WITH GIVEN LENGTH FROM POINT tool to create two sides of the rhombus, each having length ‘side’, as shown below. (Hint: Just type ‘side’ in the length box of the prompt.)
   
   
   
   -- Use the CIRCLE WITH CENTER AND RADIUS tool to construct two circles, as shown below, each with radius ‘side’.
   -- Construct the intersection point of these two circles.
   
   
   -- Finish and label the construction as shown below:
   
   
7. Construct and label an arbitrary SQUARE, as indicated below:
   
   
8. Construct and label an arbitrary PARALLELOGRAM, as indicated below:
   
   
   -- Hint: Use the ‘Slope’ command in the COMMAND MENU.
9. Construct and label an arbitrary TRAPEZOID, as indicated below:
   
   
10. SAVE your GeoGebra file with YOUR NAME, like this:
    Carol_Fisher.ggb -- Be sure to put the ‘.ggb’ extension.
    -- Use an underscore between your first and last name.
    -- This file can be emailed to an instructor (as an attachment).

When you're done playing with GeoGebra,
move on to:
‘If... Then...’ Sentences