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3/22/2014 Lesson 02.06: Module Two Activity - Create Triangles Independently

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Create Triangles Independently

"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 AcuteGo to Top Close | Print

3/22/2014 Lesson 02.06: Module Two Activity - Create Triangles Independently

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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.

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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

3/22/2014 Lesson 02.06: Module Two Activity - Create Triangles Independently

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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

3/22/2014 Lesson 02.06: Module Two Activity - Create Triangles Independently

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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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