Question

4. In the adjoining figure, A and B are two points outside a given linel, C is the midpoint of AB; AD II, BEI land CF
I I meet I at D, E and F respectively. Prove that Fis the midpoint of DE.
B
С
А.
D
F
E​

Answer 1

Answer:

Consider △ AFE and △ DFE Using the midpoint theorem AF = ½ AB = ED AE = ½ AC = FD FE is common i.e. FE = EF By SSS congruence criterion △ AFE ≅ △ DFE ∠ A = ∠ FDE (c. p. c. t) In the same way we get ∠ B = ∠ DEF and ∠ C= ∠ DFE. Therefore, it is proved that ∠ EDF = ∠ A, ∠ DEF = ∠ B and ∠ DFE = ∠ C.Read more on Sarthaks.com - https://www.sarthaks.com/726001/in-the-adjoining-figure-d-e-f-are-the-midpoints-of-the-sides-bc-ca-and-ab-respectively-of-abc?show=726002#a726002