Math, asked by nidhi291, 1 year ago

In a right angled triangle BAC, angle BAC = 90 degree, segments AD, BE and CF are the medians. Prove that 2 (AD square + BE square + CF square) = 3 BC square. ​


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Answers

Answered by ariestheracer
67

Draw right angle triangle ABC,

draw medians. AD, BE, CF. Now Join DF.

Since D and F are midpoints of sides AB and BC, DF will be parallel to AC and is equal to 1/2 AC.

ADF, ABE, AFC are all right angle triangles.

LHS,

=2( {AD}^{2}  +  {BE}^{2}  +  {CF}^{2}

=2[( {AF}^{2}  +  {DF}^{2} ) + ( {AB}^{2}  +  {AE}^{2} ) + ( {AF}^{2}  +  {AC}^{2} )]

=2(( \frac{ {AB}^{2} }{4}  +  { \frac{ {AC}^{2} }{4} }) + ( {AB}^{2}  +  {AC}^{2} ) + ( \frac{ {AC}^{2} }{4}  +  \frac{ {AB}^{2} }{4} ))

=2(  \frac{ {bc}^{2}}{2} +  {bc}^{2})

=3( {bc}^{2}  )

Answered by balu143
9

Answer:

Step-by-step explanation:

Draw right angle triangle ABC,

draw medians. AD, BE, CF. Now Join DF.

Since D and F are midpoints of sides AB and BC, DF will be parallel to AC and is equal to 1/2 AC.

ADF, ABE, AFC are all right angle triangles.

LHS,

=

=

=

=

=


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