State the following statement is True or False
The statement of Thales theorem is - "If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side."

True

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False

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Solution

The correct option is B False

Statement of the Thales theorem is - "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 $△ A B C$ if $D E | | B C$ and intersects $A B$ in $D$ and $A C$ in $E$ then
$\frac{A D}{D B} = \frac{A E}{E C}$

Hence the given statement is not Thales theorem.
Thus, the given sentence is false.

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Similar questions

Q. Prove that "If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side".

Q. Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

Theorem 6.2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Match the following table:

$\begin{matrix} Theorem Statement & Theorem Name (a) The line segment joining the mid-points of & (i) Basics proportionality theorem two sides of a triangle is parallel to the third side (b) A line parallel to one side of a triangle divides & (ii) Mid point theorem the other two sides into parts of equal poportion (c) If a line divides the any tw o sides of a triangle & (iii) Converse of Basic porpotionality theorem in the same ratio, then the line must be parallel to the third side. \end{matrix}$

Q. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the _______ side.

Q. Prove that If a line divides any two sides of a triangle in the same ratio,then the line is parallel to same side.

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State the following statement is True or FalseThe statement of Thales theorem is - "If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side."

State the following statement is True or False
The statement of Thales theorem is - "If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side."