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Similar Right Triangles

Similar Right Triangles. 1. When we use a mirror to view the top of something……. Similar Right Triangles. Eddie places a mirror 500 meters from a large Iron structure. 1. When we use a mirror to view the top of something……. (mirror). Similar Right Triangles.

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Similar Right Triangles

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  1. Similar Right Triangles 1. When we use a mirror to view the top of something…….

  2. Similar Right Triangles Eddie places a mirror 500 meters from a large Iron structure 1. When we use a mirror to view the top of something……. (mirror)

  3. Similar Right Triangles Eddie places a mirror 500 meters from a large Iron structure His eyes are 1.8 meters above the ground 1. When we use a mirror to view the top of something……. (mirror)

  4. Similar Right Triangles Eddie places a mirror 500 meters from a large Iron structure His eyes are 1.8 meters above the ground 1. When we use a mirror to view the top of something……. He stands 2.75 meters behind the mirror and sees the top (mirror)

  5. Similar Right Triangles Eddie places a mirror 500 meters from a large Iron structure His eyes are 1.8 meters above the ground 1. When we use a mirror to view the top of something……. He stands 2.75 meters behind the mirror and sees the top x 1.8 m 500 m 2.75 m

  6. Similar Right Triangles Since the triangles are similar……. x 1.8 = 500 2.75 The triangles are similar by Angle-Angle (AA) x 1.8 m 500 m 2.75 m

  7. Similar Right Triangles Since the triangles are similar……. x 1.8 = 500 2.75 . x = 500 1.8 2.75 The triangles are similar by Angle-Angle (AA) x 1.8 m 500 m 2.75 m

  8. Similar Right Triangles Since the triangles are similar……. x 1.8 = 500 2.75 . x = 500 1.8 2.75 The triangles are similar by Angle-Angle (AA) x x = 328 m 1.8 m 500 m 2.75 m

  9. Similar Right Triangles But since the triangles are similar we could equally say… x 500 = 1.8 2.75 . x = 500 1.8 2.75 The triangles are similar by Angle-Angle (AA) x x = 328 m 1.8 m 500 m 2.75 m

  10. Similar Right Triangles At a certain time of day, a lighthouse casts a 200 meter shadow 2. Now try another one………..

  11. Similar Right Triangles At a certain time of day, a lighthouse casts a 200 meter shadow At the same time Eddie casts A 3.1 meter shadow. 2. Now try another one………..

  12. Similar Right Triangles At a certain time of day, a lighthouse casts a 200 meter shadow At the same time Eddie casts A 3.1 meter shadow. 2. Now try another one……….. His head is 1.9 meters above the ground How high is the Lighthouse?

  13. Similar Right Triangles At a certain time of day, a lighthouse casts a 200 meter shadow At the same time Eddie casts A 3.1 meter shadow. 2. Now try another one……….. His head is 1.9 meters above the ground x How high is the Lighthouse? 1.9 m 3.1 m 200 m

  14. Similar Right Triangles x 1.9 = 200 3.1 . x = 200 1.9 3.1 The triangles are similar by Angle-Angle (AA) x = 123 m x 1.9 m 3.1 m 200 m

  15. Section 10-3: • Theorem 10 - 3: “The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original and each other”

  16. Section 10-3: • Theorem 10 - 3: “The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original and each other” B D A C

  17. A A B D B D C D B C ΔABC ~ ΔADB ~ ΔBDC

  18. A Similar Triangles, so……. ADBD BDCD A = B D B D C D B C ΔABC ~ ΔADB ~ ΔADC

  19. A COROLLARY 1 ADBD BDCD A = B D B D C D B C BD is the geometric mean of AD and CD

  20. Corollary 1: The altitude to the hypotenuse is the geometric mean of the two sections it splits the hypotenuse into • The altitude to the hypotenuse of ΔABC is 4 cm • If the distance AD is 2 cm, find the distance CD. B D A C

  21. Corollary 1: The altitude to the hypotenuse is the geometric mean of the two sections it splits the hypotenuse into • The altitude to the hypotenuse of ΔABC is 4 cm • If the distance AD is 2 cm, find the distance CD. • . x = 4 4 . x 4 = 4 2 2 B 4 cm x cm 2 cm D A C

  22. Corollary 1: The altitude to the hypotenuse is the geometric mean of the two sections it splits the hypotenuse into • The altitude to the hypotenuse of ΔABC is 4 cm • If the distance AD is 2 cm, find the distance CD. • . x = 4 4 • . x = 8 cm . x 4 = 4 2 2 B 4 cm x cm 2 cm D A C

  23. Corollary 1: The altitude to the hypotenuse is the geometric mean of the two sections it splits the hypotenuse into • The altitude to the hypotenuse of ΔABC cuts AC into sections that are 4 cm long and 5 cm long • Find the area of ΔABC B D A C

  24. COROLLARY 2 ACBC BCCD AND ACAB ABAD A A = B D D B B D C D B C ΔABC ~ ΔADB ~ ΔBDC

  25. Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse • The altitude to the hypotenuse of ΔABC cuts AC into sections that are 3 cm long and 6 cm long • Find the length of the legs AB and BC. B D A C

  26. Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse • Find the length of the legs AB and BC. • Hypotenuse, AC = 9 cm B y x 3 cm 6 cm D A C

  27. Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse • Find the length of the legs AB and BC. • Hypotenuse, AC = 9 cm B y x 3 cm 6 cm D A C

  28. Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse • Find the length of the legs AB and BC. • Hypotenuse, AC = 9 cm B y x 3 cm 6 cm D A C

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