Question

inverse Pythagoras theorem​

Answer 1

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.

Answer 2

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.