थेल्स प्रमेय(BPT) का कथन लिखकर उसे सिद्ध कीजिए plz help
Answers
Given : थेल्स प्रमेय(BPT) Thales theorem
To Find : Prove it
Solution:
Thales's theorem :
If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionately.
Its also called BPT : Basic proportionality theorem.
In ΔABC , DE || BC
Join D and C, and E and B.
Draw EL perpendicular to AB, and DN perpendicular to AC
Area of ΔADE /Area of ΔBDE = (1/2 * AD * EL) / (1/2 * DB * EL) = AD/ DB
Area of ΔADE /Area of ΔCDE = (1/2 * AE * DN) / (1/2 * ED * DN) = AE/ EC
area of ΔBDE = area of ΔCDE ( triangle on the same base between parallel lines)
=> Area of ΔADE /Area of ΔBDE = Area of ΔADE /Area of ΔCDE
Hence AD/DB = AE/EC
DE || BC Hence AD/DB = AE/EC
Thales theorem verified
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