# Capella University Geometry T

## Print

Print these directions.

“We interrupt your regular programming to bring you a special report. This is Carl Sterns, news anchor for Channel 1. Thirty minutes ago, the 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 Acute Perps. According to police sources, the gang robs three locations in three days and then goes unseen for weeks before they strike again. Because this is their third robbery, officials expect the robbers will go underground for the next few weeks. However, the police need the help of Geo City citizens in the meantime.”

“This gang traditionally hits the three locations during each crime spree using the same pattern. Police are asking citizens to predict the next three locations Acute Perps will attack. They will use the information to stake out these locations in the coming weeks and bring Acute Perps to justice. Back to you, Carl.”

“Thanks, Stuart. It looks like the city has some important work to do!”

You have been asked by the police to find one of the 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. Choose one of the following scenarios to help locate the gang:

• Obtuse Scalene Triangle Translation to prove SSS Congruence
• Isosceles Right Triangle Reflection to prove ASA Congruence
• Equilateral Equiangular Triangle Rotation to prove SAS Congruence

After you have selected the one transformation you will be completing, go to step 2 for detailed directions.

First, construct a triangle as indicated by your choice in step 1 on a coordinate plane. For example, if you chose to use an obtuse scalene triangle translation to prove SSS Congruence, then you will construct an obtuse scalene triangle. Make sure to measure your triangle’s angles and sides. You can use the concept of distance and slope to ensure your triangle satisfies the criteria indicated by your choice. Write down the original coordinates of this triangle.

Next, identify and label three points on the coordinate plane that are the transformation of your original triangle. Make sure you use the transformation indicated within the scenario you selected. For example, if you chose to use an obtuse scalene triangle translation to prove SSS Congruence, then you complete a translation of your triangle. Remember, you only need to complete one transformation on your triangle. Write down these new coordinates for this second triangle.

• If you chose Obtuse Scalene Triangle Translation to prove SSS Congruence, use the coordinates of your transformation 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.
• If you chose Isosceles Right Triangle Reflection to prove ASA Congruence, 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.
• If you chose Equilateral Equiangular Triangle Rotation to prove SAS Congruence, 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 must submit the construction of the original triangle and your transformation. You may create this graph using graphing technology. You may also print and use graph paper.

Provide an answer to the questions that match your selected scenario. Because you only completed one scenario, only one group of questions should be answered in complete sentences and submitted with your work.

#### Obtuse Scalene Triangle Translation to prove SSS Congruence

1. Describe the translation you performed on the original triangle. Use details and coordinates to explain how the figure was transformed, including the translation rule you applied to your triangle.
2. What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle’s measurements.
3. Did your triangle undergo rigid motion? Explain why.

#### Isosceles Right Triangle Reflection to prove ASA Congruence

1. Answer the following questions:
1. What line of reflection did you choose for your transformation?
2. How are you sure that each point was reflected across this line?
3. What reflection rule did you apply to your triangle?
2. What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle’s measurements.
3. Did your triangle undergo rigid motion? Explain why.

#### Equilateral Equiangular Triangle Rotation to prove SAS Congruence

1. Answer the following questions:
1. How many degrees did you rotate your triangle?
2. In which direction (clockwise, counterclockwise) did it move?
3. What rotation rule did you apply to your triangle?
2. What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle’s measurements.
3. Did your triangle undergo rigid motion? Explain why.

Submit the following to your instructor using a word processing document or by copying and pasting into the assignment box. You may scan, save, or take a digital picture of your construction.

• Your construction of your original triangle and your transformation
• The three ordered pairs, with labels, of both the original and congruent triangles you created using your transformation (Make sure to indicate which scenario was chosen.)
• All work for any corresponding sides using the distance formula, and clear labels
• All work for any corresponding angles (shown by use of a compass and straightedge or the slope formula)
• The answer to the questions that match your scenario

Note: Please submit the written portion of this assignment using a word processing document or by copying and pasting into the assignment box.

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