# L and M are the mid-points of AB and BC respectively of ΔABC, right-angled at B. Prove that 4LC2 = AB2 + 4BC2

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

(AB)2 + 4(BC)2 = 4(LC)2

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality Theorem42 mins
A Peep into Pythagoras Theorem43 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
Quiz | Criterion of Similarity of Triangle45 mins
How to Ace Maths in NTSE 2020?36 mins
Know About Important Proofs in Triangles33 mins
Master BPT or Thales Theorem39 mins
R.D Sharma | Solve Exercise-4.545 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses