Altitude on Hypotenuse Theorem

[neno89]

Hello. I need help prving this proof. Here is the Picture.

Given: FG is perpendicular to GH. Angle 1 is complementaryto angle 3.

Prove: JH/GH = GH/HF (they are porportions)

Please someone help me prove this! Thank you![/u]

 

[skeeter]

show that triangle GJH is similar to triangle FGH using angle-angle.

 

[zerodegrees]

Given: FG is perpendicular to GH. Angle 1 is complementaryto angle 3.

this means that angle 3 and angle 4 are complementary as well (perpendicular angles makes right angles, which leads to complementary angles)

so.....

angle 3 + angle 4=90
angle 3 + angle 1=90

substitute, angle 4 and angle 1 should be equal.

also if angle 1 is congruent to angle 2 (vertical), then you could substitute again, then angle 2+angle 3 =90. this helps because if angle GJH + angle 2 + angle 3 =180 (def triangle), when you subtract angle 2 and angle 3 from the left side of the equation and 90 degrees from the right side of the equation, then, angle GJH will equal 90 degrees, making it congruent to the right angle FGH.

that should be enough to prove your AA similarity. i hope this helps