Question

State and prove Thales theorem (Basic Proportionality Theorem).​

Answer 1

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. and DE intersects AB and AC at D and E respectively.

Answer 2

To prove the Thales theorem, draw a perpendicular bisector of ∠

Let point M be the midpoint point of line AC.

Also let ∠MBA = ∠BAM = β and ∠MBC =∠BCM =α

Line AM = MB = MC = the radius of the circle.

ΔAMB and ΔMCB are isosceles triangles.

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