IN TRIANGLE ABC D,E,F ARE MID POINTS OF SIDES AB,BC,AC SHOW THAT AE AND DF BISECT EACH OTHER - Maths - Compound Interest

Question

IN TRIANGLE ABC D,E,F ARE MID POINTS OF SIDES AB,BC,AC SHOW THAT AE
AND DF BISECT EACH OTHER

Shruti Tyagi · Accepted Answer

Dear Student,

Please find below the diagram of the problem
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_59a17ce131a16%20jpg"
style="width: 322px; height: 202px;">
Construction: Join DF,DE,EF and AEit is given that D,E,F are mid points of AB,BC and AC respectively
hence ADBD=AFFC=BEEC=11By mid point theoremthe line joining the mid points of two sides of a triangle is parralel to third side and equal to half of itHence DF∥BC, DE∥AC and EF∥ABhence ADEF is a parallelogram as DE∥AF and EF∥ADAE and DF are diagonals of a parallelogram ADEF
As we know the diagonals of a paralleogram bisect each otherTherefore AE bisects DF

Regards,