Question

Prove Thales Theorem?


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Anushka ❤ ThePrinceAryan ​

Answer 1

Basic 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

Reasons

1) EF ┴ BA

1) Construction

2) EF is the height of ∆ADE and ∆DBE

2) Definition of perpendicular

3)Area(∆ADE) = (AD .EF)/2

3)Area = (Base .height)/2

4)Area(∆DBE) =(DB.EF)/2

4) Area = (Base .height)/2

5)(Area(∆ADE))/(Area(∆DBE)) = AD/DB

5) Divide (4) by (5)

6) (Area(∆ADE))/(Area(∆DEC)) = AE/EC

6) Same as above

7) ∆DBE ~∆DEC

7) 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 equal

9) AD/DB =AE/EC

9) From (5) and (6) and (7)

Answer 2

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• Proof on Thales theorem :
• 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.