Question

. In the given figure AD and BE are the medians of AABC and BE|| DE
prove that CF =1/4 AC.
А
E
F
B В
D
C​

Answer 1

Step-by-step explanation:

In ΔBEC, D is mid-point of BC and from converse of mid-point theorem. i.e. A line i.e. DF drawn through the mid-point D of BC and parallel to BE bisects the third side i.e. EC at F. Now, F becomes the mid-point of CE. ⇒ CF = 1212 CE CF = 1212 (1212 AC) [E is mid-point of AC ⇒ AE = EC = 1212 AC] ⇒ CF = 1414 AC Hence proved.Read more on Sarthaks.com - https://www.sarthaks.com/784400/in-the-given-figure-ad-and-be-are-medians-of-abc-and-be-df-prove-that-cf-1-4ac