Theorems for TRIANGLES...

THEOREM:1(FUNDAMENTAL THEOREM OF PROPORTIONALITY)

STATEMENT: A line drawn parallel to a side of a triangle intersects the other two sides in two distinct points so that each of these sides becomes union of two line segments.The lengths of line segments of each side lying in the same semi-plane of that line are proprtional to the lengths of the corresponding sides.

DATA: In Triangle ABC, l is parallel to line segment BC. l intersects line segment AB and line segment AC in D and E respectively.

TO PROVE: (1) AD/AB=AE/AC
(2)BD/AB=EC/AC

PROOF:Construct Line Segment BE and Line Segment CD . Also Let Line segment EF be Perpendicular to Line AB and Line Segment DN be Perpendicular to Line AC. F belongs to Line AB and N belongs to Line AC.

Area of Triangle ADE=1/2 * base * Altitude.

=1/2 * AD * EF ..........................................................................eq.1

ARea of Triangle DBE = 1/2 * base * Altitude.

=1/2 * BD * EF ..........................................................................eq.2




More theorems...7,8,9,10,11.(COMING SOON!!!!)