BPT theorem Thales theorem
Answers
Answer:
In geometry, Thales' 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:-
PROOF OF BPT
Given: In ΔABC, DE is parallel to BC
Line DE intersects sides AB and AC in points D and E respectively.
To Prove: => AD/DB = AE/AC
Construction: Draw EF ⟂ AD and DG⟂ AE and join the segments BE and CD.
Proof:
Area of Triangle= ½ × base × height
In ΔADE and ΔBDE,
=> Ar(ADE) / Ar(DBE)
= ½ ×AD×EF / ½ ×DB×EF
= AD / DB ......(1)
In ΔADE and ΔCDE,
=> Ar(ADE)/Ar(ECD)
= ½×AE×DG / ½×EC×DG
= AE/EC ........(2)
Note => that ΔDBE and ΔECD have a common base DE and lie between the same parallels DE and BC. Also, we know that triangles having the same base and lying between the same parallels are equal in area.
So, we can say that
Ar(ΔDBE)=Ar(ΔECD)
Therefore,
A(ΔADE)/A(ΔBDE)
= A(ΔADE)/A(ΔCDE)
Therefore,
=> AD/DB = AE/AC
Hence Proved.
i hope it helps you.
