please tell me who are intelligent in school students please answer this
show that the square of the hypotenuse of a right angled triangle is equal in area to the sum of squares on other sides
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please tell me who are intelligent in school students please answer this
show that the square of the hypotenuse of a right angled triangle is equal in area to the sum of squares on other sides
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Answer:
I AM NOT VERY INTEGENT BUT I GET GOOD MARKS LIKE 37 OUT OF 40
Figure is in the attachment
Given:
A right angled ∆ABC, right angled at B
To Prove- AC²=AB²+BC²
Construction: draw perpendicular BD onto the side AC .
Proof:
We know that if a perpendicular is drawn from the vertex of a right angle of a right angled triangle to the hypotenuse, than triangles on both sides of the perpendicular are similar to the whole triangle and to each other.
We have
△ADB∼△ABC. (by AA similarity)
Therefore, AD/ AB=AB/AC
(In similar Triangles corresponding sides are proportional)
AB²=AD×AC……..(1)
Also, △BDC∼△ABC
Therefore, CD/BC=BC/AC
(in similar Triangles corresponding sides are proportional)
Or, BC²=CD×AC……..(2)
Adding the equations (1) and (2) we get,
AB²+BC²=AD×AC+CD×AC
AB²+BC²=AC(AD+CD)
( From the figure AD + CD = AC)
AB²+BC²=AC . AC
Therefore, AC²=AB²+BC²
This theroem is known as Pythagoras theroem