Question

ABC is an isosceles triangle such that AB=AC=10 cm and BC=16 cm.if G is the median of angle ABC.find AG

Answer 1

AB=AC=10CM
BC=16CM
IN ∆ABG&∆ACG
AB=AC
BG=CG=BC/2=8CM. AS AG IS MEDIAN
AG=AG
:. ∆ABG CONGRUENT ∆ACG
ANGLE AGB= ANGLE AGC
:.ANGLE AGB+ ANGLE AGC =180°(LINEAR PAIR)
ANGLE AGB= ANGLE AGC=90°
:.∆ABG IS RIGHT ANGLED TRIANGLE
AB^2=AG^2+BG^2
10^2=AG^2+8^2
100-64=AG^2
AG=√36=6CM