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Triangle Proportionality Theorem

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Math diagram

If D E ¯ B C ¯ , then A D D B = A E E C .

Example :

Find the value of x .

Math diagram

The lines Q R ¯ and S T ¯ are parallel.

Therefore, by the Triangle Proportionality Theorem,

P S Q S = P T R T

Substitute the values and solve for x .

6 2 = 9 x

Cross multiply.

6 x = 18

Divide both sides by 6 .

6 x 6 = 18 6 x = 3

The value of x is 3 .



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