InterviewSolution
Saved Bookmarks
| 1. |
In a triangle ABC, E is the midpoint of median AD. Show that ar ΔABE = ar ΔACE |
|
Answer» In ΔABC; AD is a median. ∴ ΔABD = ΔACD …………….. (1) (∵ Median divides a triangle in two equal triangles) Also in ΔABD; BE is a median. ∴ ΔABE = ΔBED = 1/2 ΔABD …………..(2) Also in ΔACD; CE is a median. ∴ ΔACE = ΔCDE = 1/2 ΔACD …………….(3) From (1), (2) and (3); ΔABE = ΔACE (OR) ΔABD = ΔACD [∵ AD is median in ΔABC] 1/2 ΔABD = 1/2 ΔACD [Dividing both sides by 2] ΔABE = ΔAEC [∵ BE is median of ΔABD, CE is median of ΔACD] Hence proved. |
|