Altitude to the Hypotenuse Theorem - Tomorrow we will use this theorem to prove the Pythagorean Theorem!
Altitude to Hypotenuse Theorem: --the alt to hypotenuse forms two smaller right triangles that will be similar to the original
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem: --let’s color the smallest triangle, blue
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem: -- next color the middle triangle red
Altitude to Hypotenuse Theorem:
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
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem
Altitude to Hypotenuse Theorem: x y c h b a
x y c h b a ? ? ?
x y c h b a x h a
x y c h b a x h a ? ? ?
x y c h b a x h a y h b
x y c h b a x h a
Altitude to Hypotenuse Theorem x y c h b a y h b
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.
Altitude to Hypotenuse Theorem x h a y h b
Altitude to Hypotenuse Theorem: x y c h b a x h a y h b
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
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.
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
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
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
4 y c 6
4 y c 6
Altitude to Hypotenuse Theorem: Sample Problem 3: Find c and h. x 6 c h 12
Altitude to Hypotenuse Theorem: Sample Problem 3: Find h and c. x 6 c h 12
Altitude to Hypotenuse Theorem: Sample Problem 3: Find h and c. x 6 c h 12