Question

Prove the thales theorem in maths

Answer 1

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Proportionality Theorem (Thales theorem): If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio. 

In ∆ABC , if DE || BC and intersects AB in D and AC in E then 
    AD       AE
   ---- = ------
    DB      EC

Proof on Thales theorem : 

If a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

Given : In ∆ABC , DE || BC and intersects AB in D and AC in E. 

Prove that : AD / DB = AE / EC 

Construction : Join BC,CD and draw EF ┴ BA and DG ┴ CA.  


Statements EF ┴ BA1) Construction2) EF is the height of ∆ADE and ∆DBE2) Definition of perpendicular3)Area(∆ADE) = (AD .EF)/23)Area = (Base .height)/24)Area(∆DBE) =(DB.EF)/24) Area = (Base .height)/25)(Area(∆ADE))/(Area(∆DBE)) = AD/DB5) Divide (4) by (5)6) (Area(∆ADE))/(Area(∆DEC)) = AE/EC6) Same as above7) ∆DBE ~∆DEC7) Both the ∆s are on the same base and 
between the same || lines.8) Area(∆DBE)=area(∆DEC)8) If the two triangles are similar their 
areas are equal9) AD/DB =AE/EC

Answer 2

Answer:

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