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Geometry

• Basic proportionality theorem:

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

Corollary: If D and E are points on the sides, AB and AC, respectively of ΔABC such that DE || BC, then

Example:

In the given figure, S and T are points on PQ and PR respectively of ΔPQR such that ST || QR.

Determine the length of PR.

Solution:

Since ST || QR, by basic proportionality theorem, we have

• Converse of basic proportionality theorem:

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

• Similar and Congruent Figures
• Two geometric figures having the same shape and size are said to be congruent figures.
• Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.

Example:

(1) All circles are similar.

(2) All equilateral triangles are similar.

(3) A…

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