Conceptual Project

Conceptual Project

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It’s your turn to be the designer! Imagine you are in charge of designing a kitchen floor made of tiles. You must create your own tiling pattern for the floor of the kitchen. The floor tile must be a rectangle or square. Your tile should be a minimum of 6 inches by 6 inches, and your work should be done on a grid. Your pattern must be created using AT LEAST one pair of congruent triangles, however for FULL credit your design needs to include a minimum of TWO UNIQUE PAIRS of congruent triangles. All congruent triangle pairs must have their vertices labeled, and measurements for all sides/angles must be given for one triangle in each pair of congruent triangles. The other triangles must have congruency marks so that the measures of the angles and sides can be directly compared. Create your tiling pattern by using word processing software, GeoGebra or Desmos, or by drawing it on a piece of graph paper. You are also required to use AT LEAST 2 colors in your design, however full credit will be given only for three or more colors. Once your tiling pattern is complete, answer the four questions below.

Guidelines for tile:

  1. Can be a square or rectangle with a minimum size of 6 by 6 inches
  2. Dimensions for your tile must be shown or given
  3. Design must be done on a graph or grid with x– and y-axes
  4. Design must include a minimum of one pair of congruent triangles
    1. Partial credit will be given for a tile with only one pair of congruent triangles
    2. Full credit will be given for a tile with two or more pairs of congruent triangles. The two pair cannot be congruent to one another.
  5. Design must use at least 2 colors.
    1. Partial credit will be given for two colors
    2. Full credit will be given for three or more colors
  6. All vertices of congruent triangles must be labeled
  7. Measures for angles/sides of one triangle from each pair of congruent triangles must be given.
    1. Do not just ‘make up numbers’. Remember to use the Pythagorean Theorem to find parts of right triangles. Or, if you do your work by hand, measure with a ruler/protractor. If you use GeoGebra it is fairly easy to find the lengths/angle measures.
  8. The second triangle in each pair must be marked with appropriate congruency markings.

Once you have created your tile pattern, answer the four questions below:

Question 1:

How can you prove your triangles are congruent by using one of the triangle congruency postulates? Provide a congruency statement for each pair of triangles that are congruent, and name the postulate you used and explain how your given measures justify your answer. This means directly compare corresponding congruent parts of the triangles. You must show which parts are congruent and their measures.

Question 2:

Could you use a different triangle congruence postulate to prove the triangles in your pattern are congruent? Which other congruence postulate can you use, and how do the measures of the corresponding parts support your answer. If there is not another congruency postulate you can use, explain why not.

Question 3:

How can you prove your congruent triangles are congruent by using a series of rigid transformations? Include each transformation and to what degree. For example, “translation up 2 units” or “reflection about the vertical axis.” Make sure if it is a series of transformations you give them in the correct order. Use congruencies of corresponding parts of the triangles to support your reply.

Question 4:

Could you use a different series of rigid transformations to prove the triangles are congruent? Describe the sequence of transformations that could be used OR explain why a different sequence would not produce congruent triangles.

Include your properly formatted image along with complete answers to the preceding four questions and upload for your teacher to grade. Use this rubric to guide your work.

Important: Save your work and responses to the activity questions in a document on your computer.

Save the document as FirstName_LastName_Geometry_Tile_ConceptualProject.