“We interrupt your regular programming to bring you a special report. This is Carl Sterns, news anchor for Channel 1. Thirty minutes ago notorious crime syndicate Acute Perps struck again at the world famous Wright bank. Street reporter Stuart Olsen is live on the scene in Geo City. Let’s go to Stuart now to find out more about these breaking developments. Stuart, what can you tell us?”
“Well, Carl, at approximately 8:30 this morning, a trio of masked men overwhelmed security forces here at the Wright bank in Geo City and robbed the bank of all its cash. This is the third robbery in as many days orchestrated by the Acute Perps. According to police sources, the gang robs three locations in three days and then goes unseen for weeks before they strike again. Since this is their third robbery, officials expect they will go underground for the next few weeks. However, they need the help of Geo City citizens in the meantime. On your screen is a map of the locations the Acute Perps have hit in the last three days.
This gang traditionally hits the three locations on each crime spree in the same pattern. Police are asking citizens to predict the next three locations the Acute Perps will attack. They will use the information to stake out these locations in the coming weeks and bring the Acute Perps to justice. Back to you, Carl.”
Thanks, Stuart. It looks like the city has some important work to do!”
Step 1: Translations and SSS
You have been asked by the police department to find three locations the Acute Perps gang is likely to hit in the coming weeks. Because the gang sticks to a triangular pattern, the locations could be a translation, reflection, or rotation of the original triangle. For this step, identify and label three points on the coordinate plane that are a translation of the original triangle. Next, use the coordinates of your translation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula and each corresponding pair of sides to receive full credit.
You may create the congruent triangle using this GeoGebra graph if you’d like. Refer to the directions if you need help with this program. You may also print and use graph paper.
Step 2: Reflections and ASA
Great work so far! The police department now needs you to take the original triangle and reflect it. For this step, you will need to identify and label three points on the coordinate plane that are a reflection of the original triangle. Next, use the coordinates of your reflection to show that the two triangles are congruent by the ASA postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge (Hint: Remember when you learned how to copy an angle?). You must show all work with the distance formula for the corresponding pair of sides and your work for the corresponding angles to receive full credit.
You may create the similar triangle using this GeoGebra graph if you’d like. Refer to the directions if you need help with this program. You may also print and use graph paper.
Step 3: Rotations and SAS
Your dectective work is almost complete! The last step the police department needs you to accomplish is rotating the triangle. For this step, you will need to identify and label three points on the coordinate plane that are a rotation of the original triangle. Next, use the coordinates of your rotation to show that the two triangles are congruent by the SAS postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge (Hint: Remember when you learned how to copy an angle?). You must show all work with the distance formula for the corresponding pair of sides and your work for the corresponding angles to receive full credit.
You may create the similar triangle using this GeoGebra graph if you’d like. Refer to the directions if you need help with this program. You may also print and use graph paper.
Step 4: What to Submit
Submit the following to your instructor using a word processing document or by copying and pasting into the assignment box. You may scan, fax, or take a digital picture of your constructions. If you used Geogebra, you must save your technology construction as a ggb file by going to the File menu and selecting “Save As” so your teacher can verify the constructions. Make sure to make each transformation its own separate graph.
1. The three ordered pairs, with labels, of the congruent translated triangle you created. All work for corresponding sides using the distance formula.
2. The three ordered pairs, with labels, of the congruent reflected triangle you created. All work for corresponding sides using the distance formula and clearly labeled. All work for corresponding angles must be shown by use of a compass and straightedge or the slope formula.
3. The three ordered pairs, with labels, of the congruent rotated triangle you created. All work for corresponding sides using the distance formula and clearly labeled. All work for corresponding angle must be shown by use of a compass and straightedge or the slope formula.
Provide answers to the following questions along with your transformations:
1. Describe the transformation you performed on the original triangle. Use details and coordinates to explain how the figure was transformed. Be sure to use complete sentences in your answer.
2. How many degrees did you rotate your triangle? In which direction (clockwise, counterclockwise) did it move? Be sure to use complete sentences in your answer.
3. What line of reflection did you choose for your transformation? How are you sure that each point was reflected across this line? Be sure to use complete sentences in your answer.
*Note: Please submit the written portion of this assignment using a word processing document or by copying and pasting into the assignment box.
“We now return you to your originally scheduled programming.”
Step 4: What to Submit
Submit the following to your instructor using a word processing document or by copying and pasting into the assignment box. You may scan, fax, or take a digital picture of your constructions. If you used Geogebra, you must save your technology construction as a ggb file by going to the File menu and selecting “Save As” so your teacher can verify the constructions. Make sure to make each transformation its own separate graph.
1. The three ordered pairs, with labels, of the congruent translated triangle you created. All work for corresponding sides using the distance formula.
2. The three ordered pairs, with labels, of the congruent reflected triangle you created. All work for corresponding sides using the distance formula and clearly labeled. All work for corresponding angles must be shown by use of a compass and straightedge or the slope formula.
3. The three ordered pairs, with labels, of the congruent rotated triangle you created. All work for corresponding sides using the distance formula and clearly labeled. All work for corresponding angle must be shown by use of a compass and straightedge or the slope formula.
Provide answers to the following questions along with your transformations:
1. Describe the transformation you performed on the original triangle. Use details and coordinates to explain how the figure was transformed. Be sure to use complete sentences in your answer.
2. How many degrees did you rotate your triangle? In which direction (clockwise, counterclockwise) did it move? Be sure to use complete sentences in your answer.
3. What line of reflection did you choose for your transformation? How are you sure that each point was reflected across this line? Be sure to use complete sentences in your answer.
*Note: Please submit the written portion of this assignment using a word processing document or by copying and pasting into the assignment box.
“We now return you to your originally scheduled programming.”
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