Question

If a line intersects sides AB and AC of ΔABC at D and E respectively and is parallel to BC,prove that AD/AB=AE/AC​

Answer 1

Answer:

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Answer 2

Hope this helps u

Given:-DE||BC
To prove:-AD/AB=AE/AC

In triangle ABC
AD/DB=AE/EC(By basic proportionality theorem)
On taking reciprocal on both the sides we get
DB/AD=EC/AE
Adding 1 on both the sides
(DB/AD)+1=(EC/AE)+1
(DB+AD)/AD=(EC+AE)/AE
AB/AD=AC/AE
Again on taking reciprocal on both the sides we get
AD/AB=AE/AC
Hence proved

Diagram is given below