Prove that is a right angle triangle, the square of the hypotenuse is equal the sum
of the squares of other two sides.
Answers
Answer:
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.
Step-by-step explanation:
ANSWER
Consider a right angled triangle with length of hypotenuse as c and the remaining two sides as a and b respectively.
We arrange 4 such triangles in such a fashion that they form a square of side a+b (as shown in the figure).
Area of the figure A= (a+b)(a+b) .......(1)
Also area of the figure can be written as, A=4×ar(Bluerighttriangle)+ar(centralyellowsquare)
A=4×
2
1
ab+c
2
.......(2)
Equating (1) and (2) we get,
c
2
+2ab=a
2
+b
2
+2ab
Consequently, c
2
=a
2
+b
2
. Hence, Pythagoras theorem is proved.
Answer:
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