inverse Pythagoras theorem
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0
Answer:
To state the "Inverse Pythagoras Theorem", draw a perpendicular from the right angle to the hypotenuse, and call its length
h
:
The inverse Pythaogoras Theorem says:
1
a
2
+
1
b
2
=
1
h
2
Proving it is straight forward:
a
r
(
△
A
B
C
)
=
a
r
(
△
A
D
C
)
+
a
r
(
△
B
D
C
)
1
2
a
b
=
1
2
h
.
A
D
+
1
2
h
.
B
D
a
b
=
h
.
(
A
D
+
B
D
)
a
b
=
h
c
c
=
a
b
h
Now, put this in Pythagoras theorem identity:
a
2
+
b
2
=
(
a
b
h
)
2
Rearranging:
1
a
2
+
1
b
2
=
1
h
2
I must have proved it many times, but looking at it with the name "Inverse Pythagoras Theorem" gave me a new respect for it.
Answered by
0
Answer:
Two light sources A and B shine onto a screen located at the triangle's right angle. As you move A and B along the hypotenuse, the green and blue triangles scale and rotate, while their opening angles stay the same.
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