Question

what is theorem 6.1 in ch triangles

Answer 1

THEROM 6.1 IS :-

( ASA congruence rule) : Two triangles are congruent is two angles and the included side of one triangle are equal to rwo angles and the included side of other triangle.

Answer 2

Thales Theorem

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

Given- a triangle ABC in which DE parallel to BC and BD intersect AB and AC at D and E respectively.

To prove- AD/ DB = AE/EC

Construction- Join BE and CD.
Draw EL perpendicular to AB and DM perpendicular to AC.

Proof - ar(triangle ADE) = 1/2 x AD x EL

ar(triangle DBE) = 1/2 x DB x EL

ar(triangle ADE) = 1/2 x AD x EL
__________________________ = AD/ --(i)
ar(triangle DBE) = 1/2 x DB x EL DB

AGAIN,
ar(triangle ADE) = 1/2 x AE x DM
__________________________ = AE/ ---(ii) ar(triangle ECD) = 1/2 x EC x DM EC

ar(triangle DBE) = ar(triangle ECD)---(iii)

from (i), (ii) and (iii)

AD/DB = AE / EC



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THANKS..