Question

In the figure, LDMN, then prove that LM2 + DN2 = LN2 + MD2

Answer 1

Given : LD ⊥ MN

To Find : prove that LM² + DN² = LN² + MD²

Solution:

  LD ⊥ MN

=> ΔMDL & ΔNDL are right angle Triangles

Using Pythagoras theorem

MD² + DL² = LM²   Eq1

DN² + DL² = LN²   Eq2

Eq2 - Eq2

=> MD² - DN²  = LM²  -  LN²  

changing sides of DN² and LN²  

=> MD² +  LN²   = LM² + DN²

=> LM² + DN² = LN² + MD²

QED

Hence Proved

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