"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!"

STEP 1: 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

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

STEP 2: First, construct a triangle as indicated by your choice in step 1 on a coordinate plane. For example, if you choose 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 choose 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.

You must submit the construction of the original triangle and your transformation. You may create this graph using graphing technology.

STEP 3: Provide an answer to the questions that match your selected scenario. A group of questions should be answered in complete sentences and submitted with your work.

Obtuse Scalene Triangle Translation to prove SSS Congruence:

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.

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.

Did your triangle undergo rigid motion? Explain why.

STEP 4:

The 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

Question

04-01-2024
Mathematics

contestada

"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!"

STEP 1: 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

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

STEP 2: First, construct a triangle as indicated by your choice in step 1 on a coordinate plane. For example, if you choose 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 choose 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.

You must submit the construction of the original triangle and your transformation. You may create this graph using graphing technology.

STEP 3: Provide an answer to the questions that match your selected scenario. A group of questions should be answered in complete sentences and submitted with your work.

Obtuse Scalene Triangle Translation to prove SSS Congruence:

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.

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.

Did your triangle undergo rigid motion? Explain why.

STEP 4:

The 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

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Step-by-step explanation:

The 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. You have chosen to use the Obtuse Scalene Triangle Translation to prove SSS Congruence. To complete this transformation, you need to construct an obtuse scalene triangle on a coordinate plane. For example, you can choose the following vertices: A(0, 0), B(4, 0), and C(0, 6) . Next, you need to translate this triangle to a new location while maintaining its shape and size. You can choose any translation you like, but for example, you can translate the triangle 3 units to the right and 2 units up. This will give you the new vertices: A'(3, 2), B'(7, 2), and C'(3, 8) . Finally, you need to prove that the two triangles are congruent by the SSS postulate. You can do this by showing that the three sides of the original triangle are congruent to the corresponding sides of the translated triangle. You can use the distance formula to calculate the length of each side of both triangles and show that they are equal. If the lengths of the three sides of the original triangle are equal to the length of the three sides of the translated triangle, then they are congruent by the SSS postulate .