In an acute triangle ABC, AL perpendicular BC. Prove that AB > BL and AC > CL. Hence deduce the
result AB + AC > BC.
Answers
Given : In an acute triangle ABC, AL perpendicular BC.
To find : Prove that AB > BL and AC > CL also AB + AC > BC.
Solution:
In an acute triangle ABC, AL perpendicular BC
=> Δ ABL is right angle triangle
AB is hypotenuse
hypotenuse is largest side of right angle triangle
( or use the fact that side opposite to largest angle is largest and 90° is largest angle )
=> AB > BL
Similarly
=> Δ ACL is right angle triangle
AC is hypotenuse
hypotenuse is largest side of right angle triangle
( or use the fact that side opposite to largest angle is largest and 90° is largest angle )
=> AC > CL
AB + BC > BL + CL
=> AB + BC > BC ( also sum of two sides of triangle is greater than third side )
QED
Proved
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