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Extra Credit Project

Extra Credit Project. __________________________________________________________. Similar Triangles in Everyday Situations. Created by: Carolina Jaramillo Period 1. Introduction. Using proportions derived from similar triangles, I will find the height of the very top of my house.

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Extra Credit Project

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  1. Extra Credit Project __________________________________________________________ Similar Triangles in Everyday Situations Created by: Carolina Jaramillo Period 1

  2. Introduction • Using proportions derived from similar triangles, I will find the height of the very top of my house.

  3. HOW WILL I DO THIS ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  4. I will place a mirror on the floor between the object and me and look into it from a specific distance from which I can view the topof the object clearly. The distances involved will be the make-up of the proportions. ? Height of house My height Distance between object and mirror Distance between mirror and me

  5. Why can I use these two triangles to set up a proportion? • Knowing about similar triangles and their shortcuts, I could use the Angle-Angle-Similarity Theorem to make sure that these two triangles are similar. • I know that <C and <O are congruent because they both are right angles and, believe it or not, ALL right angles are congruent. • Also, I know that <FAC and <EAO are congruent because mirrors reflect off light at the same angle that light hits it. • Therefore: ΔFCA ~ ΔEOA E F C O A

  6. Using the statementΔFCA ~ ΔEOA, I will set up a proportion in which the corresponding sides will be in place. I will use “x” in the proportion to denote the height of my house. E My height corresponds to the house’s height. My distance from the mirror corresponds to the house’s distance from the mirror. F My height = Me to mirror House’s heightHouse to mirror C O A

  7. Measuring Distances I went outside and took my 2-foot ruler to begin my measuring...

  8. mirror ruler me

  9. notes

  10. More measurements!

  11. As I continued my measurements...

  12. ...my doggy slept! ZZZZZZZZ...

  13. ...later, he woke up to watch me What in the dog-world is she measuring???

  14. That project looks hard...

  15. That’s too much math for me...

  16. Anyway… getting back to the project…

  17. ♫ Plug it in, Plug it in ♫ … My height = Me to mirror House’s heightHouse to mirror • 57 = 31 • x 264 Substitution Now, cross-multiply and come up with a simple equation: 57(264) = 31(x) 15048 = 31x Simplify 485.4193548 = x Division Prop. of equality 485 inches = x Round ***Note: all measurements are in inches

  18. As you saw, I used a proportion to find the height of my house. Height: About 485 inches -or- about 40 feet

  19. The End

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