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

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

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

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

5. Similar Right Triangles 1. When we use a mirror to view the top of something……. Eddie places a mirror 500 meters from a large Iron structure His eyes are 1.8 meters above the ground He stands 2.75 meters behind the mirror and sees the top x 500 m2.75 m 1.8 m

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

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

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

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

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

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

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

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

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

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” A B C D

18. A BC D D A B D B C ΔABC ~ ΔADB ~ ΔBDC

19. A BC D D A B D B C Similar Triangles, so……. AD BD BD CD = ΔABC ~ ΔADB ~ ΔADC

20. A BC D D A B D B C BD is the geometric mean of AD and CD COROLLARY 1 AD BD BD CD =

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

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

23. 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 Corollary 1: The altitude to the hypotenuse is the geometric mean of the two sections it splits the hypotenuse into A B C D 4 cm 2 cm x 4 4 2 = x cm 2.

24. 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 Corollary 1: The altitude to the hypotenuse is the geometric mean of the two sections it splits the hypotenuse into A B C D

25. A BC D D A B D B C ΔABC ~ ΔADB ~ ΔBDC COROLLARY 2 AC BC BC CD AND AC AB AB AD D B =

26. 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. Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse A B C D

27. Find the length of the legs AB and BC. Hypotenuse, AC = 9 cm Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse A B C D 3 cm6 cm x y

28. Find the length of the legs AB and BC. Hypotenuse, AC = 9 cm Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse A B C D 3 cm6 cm x y

29. Find the length of the legs AB and BC. Hypotenuse, AC = 9 cm Corollary 2: Each leg of the large triangle is the geometric mean of the hypotenuse and the adjacent segment of hypotenuse A B C D 3 cm6 cm x y