altitude to the hypotenuse theorem - tomorrow we will use this theorem to prove the pythagorean...
TRANSCRIPT
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:
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem:
Altitude to Hypotenuse Theorem
Altitude to Hypotenuse Theorem
Altitude to Hypotenuse Theorem
Altitude to Hypotenuse Theorem
Altitude to Hypotenuse Theorem
Altitude to Hypotenuse Theorem:
x
y
c
h
b
a
Altitude to Hypotenuse Theorem:
x
y
c
h
b
a
?
?
?
Altitude to Hypotenuse Theorem:
x
y
c
h
b
a
x
h
a
Altitude to Hypotenuse Theorem:
x
y
c
h
b
a
x
h
a
?
?
?
Altitude to Hypotenuse Theorem:
x
y
c
h
b
a
x
h
a
y
h
b
Altitude to Hypotenuse Theorem:
x
y
c
h
b
a
x
h
ac aa x
Altitude to Hypotenuse Theorem
x
y
c
h
b
a
y
h
bc byb
Altitude to Hypotenuse Theorem: either leg of the large triangle is the geom mean of
x
yh
b
a
c byb
c aa x
• the entire hypotenuse and
• the segment of the hyp adjacent to that leg.
Altitude to Hypotenuse Theorem
x
h
a
y
h
bx hyh
Altitude to Hypotenuse Theorem:
x
y
c
h
b
a
x
h
a
y
h
bx hyh
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
x hyh
Altitude to Hypotenuse Theorem:1. Alt to hyp forms 3 ~ rt triangles2. 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
yc
h
b
a x hyh
3. the alt to the hyp is the geom mean of the two segments of the hypotenuse.
c byb
c aa x
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
x10
6
c byb
c aa x
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
x10
6
c byb
c aa x
10 66 x
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
yc
6
x hyh
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
yc
6
x hyh
4 66 y
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
yc
6
x hyh
4 36
9
4 9 13
4 66
y
y
c
y
Altitude to Hypotenuse Theorem:Sample Problem 3: Find c and h.
x
6c
h12
Altitude to Hypotenuse Theorem:Sample Problem 3: Find h and c.
x
6
c
h12
6 144
24
24 6 18
1212 6c
c
x
c
Altitude to Hypotenuse Theorem:Sample Problem 3: Find h and c.
x
6
c
h12
6 144
24
24 6 18
1212 6c
c
x
c
2 108
108 6 3
186
h
h
hh