state and prove Thalis theorem?
Answers
Step-by-step explanation:
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.
ANSWER
Statement: If a line is drawn parallel to one side of a triangle, to interest the other two sides at indistinct points, the other two sides are divided in the same ratio.
Given: - In △ABC,DE∥BC
To prove:- AD/DB = AE/EC
Construction:- BE and CD are joined. EF⊥AB and DN⊥AL
are drawn.
Proof:-
ar(△ADE) = 1/2×AD×EF
=1/2×AE×DN
ar(△BDE) = 1/2×BD×EF
ar(△CDE) = 1/2×EC×DN
ar(△ADE)/ar(△BDE) = 1/2×AD×EF/1/2×BD×EF ........(1)
ar(△ADE)/ar(△CDE) = 1/2×AE×DN/1/2×EC×DN ........(2)
But, ar(△BDE) = ar(△CDE) ..............(3)
as they are on the same base DE and DE∥BC
from (1), (2) and (3) we get AD/DB = AE/EC
Step-by-step explanation:
Hope it helps