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Altitude to the Hypotenuse Theorem - Tomorrow we will use this theorem to prove the Pythagorean Theorem!

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Presentation on theme: "Altitude to the Hypotenuse Theorem - Tomorrow we will use this theorem to prove the Pythagorean Theorem!"— Presentation transcript:

1 Altitude to the Hypotenuse Theorem - Tomorrow we will use this theorem to prove the Pythagorean Theorem!

2 Altitude to Hypotenuse Theorem: --the alt to hypotenuse forms two smaller right triangles that will be similar to the original

3 Altitude to Hypotenuse Theorem:

4 Altitude to Hypotenuse Theorem: --let’s color the smallest triangle, blue

5 Altitude to Hypotenuse Theorem:

6 Altitude to Hypotenuse Theorem: -- next color the middle triangle red

7 Altitude to Hypotenuse Theorem:

8 Altitude to Hypotenuse Theorem: --now let’s move & rotate the two small triangles to study all three at the same time in the same orientation

9 Altitude to Hypotenuse Theorem:

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17 Altitude to Hypotenuse Theorem

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22 Altitude to Hypotenuse Theorem: x y c h b a

23 x y c h b a ? ? ?

24 x y c h b a x h a

25 x y c h b a x h a ? ? ?

26 x y c h b a x h a y h b

27 x y c h b a x h a

28 Altitude to Hypotenuse Theorem x y c h b a y h b

29 Altitude to Hypotenuse Theorem: either leg of the large triangle is the geom mean of x y h b a the entire hypotenuse and the segment of the hyp adjacent to that leg.

30 Altitude to Hypotenuse Theorem x h a y h b

31 Altitude to Hypotenuse Theorem: x y c h b a x h a y h b

32 Altitude to Hypotenuse Theorem: --the alt to the hypotenuse is the geometric mean of the two segments of the hypotenuse. x y c h b a

33 Altitude to Hypotenuse Theorem: 1. Alt to hyp forms 3 ~ rt triangles 2.either leg of the large triangle is the geom mean of the entire hyp and the segment of the hyp adjacent to that leg.  and  x y c h b a 3.the alt to the hyp is the geom mean of the two segments of the hypotenuse. 

34 Altitude to Hypotenuse Theorem: Sample Problem 1: (use part 2 of theorem) 2.either leg of the large triangle is the geom mean of the entire hyp and the segment of the hyp adjacent to that leg.  and  x 10 6

35 Altitude to Hypotenuse Theorem: Sample Problem 1: (use part 2 of theorem) 2.either leg of the large triangle is the geom mean of the entire hyp and the segment of the hyp adjacent to that leg.  and  x 10 6

36 Altitude to Hypotenuse Theorem: Sample Problem 2: (use part 3 of theorem) 2.the alt to the hyp is the geom mean of the two segments of the hypotenuse.  4 y c 6

37 4 y c 6

38 4 y c 6

39 Altitude to Hypotenuse Theorem: Sample Problem 3: Find c and h. x 6 c h 12

40 Altitude to Hypotenuse Theorem: Sample Problem 3: Find h and c. x 6 c h 12

41 Altitude to Hypotenuse Theorem: Sample Problem 3: Find h and c. x 6 c h 12


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