Question

L and M are the mid-points of the sides AB and AC of triangle ABC, right angled at B.
Show that 4LC² = AB²+ 4 BC²​

Answer 1

Step-by-step explanation:

Given: ABC is a right triangle right angled at B and L and M are the mid-points of AB and BC respectively.

⟹AL=LB and BM=MC

In △LBC, using Pythagoras theorem we have,

(Perpendicular)

2

+ (Base)

2

= (Hypotenuse)

2

⟹(LB)

2

+(BC)

2

=(LC)

2

⟹(

2

AB

)

2

+(BC)

2

=(LC)

2

⟹(AB)

2

+4(BC)

2

=4(LC)

2