how does a median divide a triangle in two congruent triangles? can you explain with an example, elaborated.

Asked by ishita605 | 2nd Jan, 2018, 08:36: PM

Expert Answer:

 
begin mathsize 16px style In space the space given space figure comma space ABC space is space straight a space traingle space and space AD space is space the space median.
Draw space AL perpendicular BC
Since space AD space is space the space median space of space triangle space ABC comma space straight D space is space the space mid minus point space of space BC.
rightwards double arrow BD equals DC
rightwards double arrow BD cross times AL equals DC cross times AL
rightwards double arrow 1 half cross times BD cross times AL equals 1 half cross times DC cross times AL
rightwards double arrow Area space left parenthesis triangle ABD right parenthesis equals Area space left parenthesis triangle ADC right parenthesis
Thus comma space median space of space straight a space triangle space divides space it space into space two space triangles space of space equal space areas.
end style

Answered by Rashmi Khot | 3rd Jan, 2018, 10:50: AM