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Exploring Congruent and Similar Figures: Transformations and Relationships

Learn about congruent and similar figures in architecture, manufacturing, and nature. Discover how transformations like translations, reflections, and rotations relate to congruency and similarity.

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Exploring Congruent and Similar Figures: Transformations and Relationships

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  1. Chapter 6 What are Congruent and Similar figures? Day 2 How are they related to Transformations?

  2. Congruent Figures

  3. What are Congruent Figures? Congruent figures.... Are figures that have the exact same shape AND size! Why learn about Congruent Figures? Let’s see…

  4. You see congruency in Architecture! World Trade Center

  5. Congruency in Architecture! Petronas Twin Towers (Malaysia’s version)

  6. Whose Twin Towers are TALLEST? Anyone have a guess? Twin Towers – New York Twin Towers - Malaysia

  7. Congruency in Architecture! Portland, Maine Convention Center and Hotel

  8. The US Department of Treasury must use congruency when it makes money!

  9. Manufacturers use congruency when making their products! Assembly Line Packaging Apple City Shopper Barbie Toy Makers

  10. Corresponding Parts of Congruent Figures Triangle ABC Triangle DEF

  11. How do TRANSFORMATIONS relate to CONGRUENCY? • Transformations that translate (slide), reflect (flip), and rotate (turn) • a figure do not change its size or shape. • Translations, reflections, and rotations ONLY change the position and orientation of a figure. • Therefore, the figure and its image are congruent. Reflection Rotation Translation congruent congruent congruent So… this being said If two figures are congruent, then a transformation (or series of transformations) will MAP one figure onto the other.

  12. Similar Figures

  13. What are Similar Figures? Similar figures.... Are figures that have the exact same shape BUT are not always the same size! However, side lengths are proportional from one shape to the next. What does similarity look like in nature? Let’s see…

  14. Similarity in Families

  15. Similarity in the Animal Kingdom

  16. always the same size.

  17. These two triangles are similar, because their ANGLE measurements are the SAME, but their SIDE lengths are DIFFERENT. Are the side lengths proportional? How can you tell? Which is the preimage and which is the image? How do you know?

  18. How do TRANSFORMATIONS relate to SIMILARITY? • A dilation is a transformation in which a figure and its image are similar. Dilation • Angles are the same • Different side lengths Similar

  19. Time for Classwork

  20. End of PowerPoint

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