BPT theorem class 10 in triangle
Answers
Basic Proportionality Theorem (B.P.T)
Statement: 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.
Given: In △ABC , line DE is drawn parallel to side BC which meets AB at D and AC at E .
To Prove:
AD /DB = AE /EC
Proof:
Statements Reasons
In △ABC and △ADE ,
∠ABC = ∠ADE Corresponding angles
∠ACB = ∠AED Corresponding angles
∠BAC = ∠DAE Common (shared angle)
∴ △ABC∼△ADE By AA∼
AB /AD = AC /AE
Corresponding sides of similar tringles are proportional
⇒
AD+DB = AE+EC
____ _____
AD AE
⇒ 1+ DB /AD =1+ EC /AE
AD /AD =1 ; AE /AE =1
⇒ DB /AD = EC /AE
Cancelling 1 from both the sides
⇒ AD /DB = AE /EC
Taking the reciprocal