I. TRANSLATIONS INVESTIGATIONS

1. Draw a scalene triangle and label the vertices.

2. Select the vertices and sides of your triangle.

3. All parts of the triangle should be selected. Choose TRANSLATE from the TRANSFORM menu.

4. In the translate box, click on RECTANGULAR VECTOR. Enter 2 for the horizontal and 3 for the vertical. Click OK.

5. Select SNAP TO GRID from the GRAPH menu. You should find that your triangle moved _____ units over and ____ units up.

6. Under the FILE menu choose NEW SKETCH. Draw another triangle and repeat the above steps. Use different numbers for the horizontal and vertical moves. Your horizontal entry is ______ and your vertical entry is _____. Your triangle moved ____ units over and ____ units up/down.

II. REFLECTIONS

1. Draw a scalene triangle and label the vertices.

2. Draw a line beside your triangle. With this line selected choose MARK MIRROR from the TRANSFORM menu. The line should flash to alert you that the command has been executed.

3. Select all parts of the triangle. Choose REFLECT from the TRANSFORM menu.

4. Draw what you see on your screen.

5. Draw a second line just below the reflection. Select it and choose MARK MIRROR from the TRANSFORM menu.

6. Select all parts of the reflected triangle. Choose REFLECT from the TRANSFORM menu.

7. Sketch what you see on your screen.

III. ROTATIONS

1. Draw a scalene triangle and label the vertices A, B, and C.

2. Use the point tool to locate a point, D, slightly below the triangle. With this point selected, choose MARK CENTER from the TRANSFORM menu.

3. Select all parts of the triangle and choose ROTATE from the TRANSFORM menu. Enter -45 for the angle of rotation.

4. Measure <ADA’, <BDB’, and <CDC’. <ADA’____ <BDB’____ <CDC’____

5. Draw a sketch of the screen.

6. Under the FILE menu choose NEW SKETCH and go through these steps again with a different triangle and a different angle of rotation. Record your angle measures and draw your sketch.

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IV. REFLECTION AND ROTATION

1. Select CREATE AXES from the GRAPH menu.

2. Draw a scalene triangle in the upper left hand quadrant and label the vertices.

3. Select the y-axis and choose MARK MIRROR from the TRANSFORM menu.

4. Select all parts of the triangle and choose REFLECT from the TRANSFORM menu.

5. On your paper, draw a sketch of what you see on your screen.

6. Select the x-axis and choose MARK MIRROR from the TRANSFORM menu.

7. Select the triangle reflection and choose REFLECT from the TRANSFORM menu.

8. Draw a sketch of the screen.

9. Select the origin. Choose MARK CENTER from the TRANSFORM menu.

10. Select the original triangle. Choose ROTATE from the TRANSFORM menu. Enter
( -180) as your angle of rotation.

11. What do you observe? Draw a sketch of the screen. You could say a reflection of a reflection is a ______________

GEOMETRY PROJECT
RIGID TRANSFORMATIONS
WITH GEOMETER’S SKETCHPAD

You are to create a design using any polygon. Your design must include a translation, a reflection, and a rotation of the polygon you have chosen as your original. You may use a maximum of two different polygons but you must include all transformations on each one. You may also use a dilation, but this is not a requirement. You will print 2 copies of your design. One copy will be your schematic diagram, showing the original, and listing each transformation and indicating its position in the design. I suggest color coding the schematic to make it easier to follow. On the other copy, you will color your design and name it. This project will be graded on its complexity, completeness, the accuracy of your schematic, and its attractiveness.