Question

in triangle abc angle C is equal to 90 degree if D and E are the points on the sides AC and BC respectively prove that AE square + BD square is equal to AB square + DE square ​

Answer 1

Answer:

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Answer 2

Answer with Step-by-step explanation:

In triangle ABC

Angle C=90 degree

In triangle ACE

$AE^2=AC^2+CE^2$...(1)

Using Pythagoras theorem

$(Hypotenuse)^2=(base)^2+(Perpendicular\;side)^2$

In triangle DCB

$BD^2=DC^2+CB^2$...(2)

In triangle ABC

$AB^2=AC^2+BC^2$...(3)

In triangle DCE

$DE^2=DC^2+CE^2$...(4)

Adding equation (1) and (2)

$AE^2+BD^2=AC^2+CE^2+DC^2+CB^2$

$AE^2+BD^2=AB^2+DE^2$

By using equation (3) and (4)

Hence, proved.

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