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Geo City citizen, 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, identify and label three points on the coordinate plane that will form a triangle congruent to the one shown on the map. 

A triangle is shown on the coordinate plane. One vertex of the triangle, located at (6, 3), is labeled Cubic Storage. Another vertex at (6, -3) is labeled Geometric Gems. The third vertex at (-2, -3) is labeled Wright Bank

You may create the congruent triangle using this GeoGebra graph if you’d like. Refer to thedirections if you need help with this program. You may also print and use graph paper.

It is possible that the gang will change their plan based on the recent news segment. Therefore, identify and label three points on the coordinate plane that create a similar triangle where the side lengths are one-halfthat of the original triangle, triangle WGC. 

A triangle is shown on the coordinate plane. One vertex of the triangle, located at (6, 3), is labeled Cubic Storage. Another vertex at (6, -3) is labeled Geometric Gems. The third vertex at (-2, -3) is labeled Wright Bank

You may create the similar triangle using this GeoGebra graph if you’d like. Refer to thedirections if you need help with this program. You may also print and use graph paper.

Write two paragraphs to answer the following questions.

  • Why did you choose those particular three locations for the congruent triangle? How did you know those points would form a triangle congruent to the given triangle? Which congruency postulate or theorem (SAS, ASA, SSS, etc.) did you use to create the congruent triangle? Why did you choose it? You must include a justification for the postulate or theorem you chose accompanied by any applicable work.
  • Why did you choose those particular three locations for the similar triangle? How did you know those points would create a triangle similar to the given triangle? Which similarity postulate or theorem (AA, SAS, SSS, etc.) did you use to create the similar triangle? Why did you choose it? You must include a justification for the postulate or theorem you chose accompanied by any applicable work.

 

            to be submitted: 

  1. The three ordered pairs, with labels, of the congruent triangle you created. Labels for each point may be as simple as A, B, C, or creative location names such as “A Cute Flower Shop.” The triangle may be included, but is not required.

  2. The three ordered pairs, with labels, of the similar triangle you created. Labels for each point may be as simple as A, B, C, or creative location names such as “A Cute Flower Shop.” The triangle may be included, but is not required.

  3. Two paragraphs to answer the given questions and justify the congruence and similarity of the triangles.

    • Why did you choose those particular three locations for the congruent triangle? How did you know those points would form a triangle congruent to the given triangle? Which congruency postulate or theorem (SAS, ASA, SSS, etc.) did you use to create the congruent triangle? Why did you choose it? You must include a justification for the postulate or theorem you chose accompanied by any applicable work.
    • Why did you choose those particular three locations for the similar triangle? How did you know those points would create a triangle similar to the given triangle? Which similarity postulate or theorem (AA, SAS, SSS, etc.) did you use to create the similar triangle? Why did you choose it? You must include a justification for the postulate or theorem you chose accompanied by any applicable work.

 

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