menu search
brightness_auto
more_vert
Pythagoras theorem with formula and proof
thumb_up_off_alt 1 like thumb_down_off_alt 0 dislike

1 Answer

more_vert
 
verified
Best answer

Pythagoras theorem 

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

\(AC^2=AB^2+BC^2\)

 Proof 

We know, △ADB ~ △ABC

Therefore, \(\tfrac{AD}{AB}=\tfrac{AB}{AC} \)(corresponding sides of similar triangles)

Or, AB= AD × AC ……………………………..……..(1)

Also, △BDC ~△ABC

Therefore, \(\tfrac{CD}{BC}=\tfrac{BC}{AC}\) (corresponding sides of similar triangles)

Or, BC2= CD × AC ……………………………………..(2)

Adding the equations (1) and (2) we get,

AB+ BC= AD × AC + CD × AC

AB+ BC= AC (AD + CD)

Since, AD + CD = AC

Therefore, AC2 = AB2 + BC2

Hence, the Pythagorean theorem is proved.

Download img file for quick revision offline

thumb_up_off_alt 1 like thumb_down_off_alt 0 dislike

Related questions

thumb_up_off_alt 0 like thumb_down_off_alt 0 dislike
1 answer
thumb_up_off_alt 0 like thumb_down_off_alt 0 dislike
1 answer
thumb_up_off_alt 0 like thumb_down_off_alt 0 dislike
1 answer
thumb_up_off_alt 1 like thumb_down_off_alt 0 dislike
1 answer
thumb_up_off_alt 0 like thumb_down_off_alt 0 dislike
1 answer
thumb_up_off_alt 1 like thumb_down_off_alt 0 dislike
1 answer

4.8k questions

4.3k answers

67 comments

388 users

...