In triangle ABC, AD is the median. Then AB + AC is _________.

Asked by gpnkumar0 | 5th Aug, 2016, 06:18: PM

Expert Answer:

begin mathsize 20px style Construction colon space Produce space AD space to space straight E space such space that space AD equals DE. space Join space CE.
Proof colon
In space increment ABD space and space increment CDE comma
AD equals DE space left parenthesis Construction right parenthesis
BD equals CD space left parenthesis AD space is space the space median right parenthesis
angle ADB equals angle CDE space left parenthesis Vertically space opposite space angles right parenthesis
increment ABD approximately equal to increment CDE... left parenthesis SAS space congruence space criterion right parenthesis
rightwards double arrow AB equals CE space left parenthesis cpct right parenthesis
In space increment ACE comma
AC plus CE greater than AE space left parenthesis Sum space of space any space two space sides space of space straight a space triangle space is space greater space than space the space third space side right parenthesis
rightwards double arrow AC plus AB greater than AD plus DE... left parenthesis from space left parenthesis straight i right parenthesis space and space straight A minus straight D minus straight E right parenthesis
rightwards double arrow AB plus AC greater than 2 AD
rightwards double arrow Then space AB plus AC space is space greater space than space 2 AD. end style

Answered by Rebecca Fernandes | 7th Aug, 2016, 10:54: AM