Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two side in distinct points, the other two sides are divided in the same ratio. Given: Ξ ABC where DE β₯ BC
To Prove: π΄π·/π·π΅ = π΄πΈ/πΈπΆ
Construction: Join BE and CD
Draw DM β₯ AC and EN β₯ AB.
Proof:
Now,
Now,
ar (ADE) = 1/2 Γ Base Γ Height
= 1/2 Γ AE Γ DM
ar (DEC) = 1/2 Γ Base Γ Height
= 1/2 Γ EC Γ DM
Divide (3) and (4)
"ar (ADE)" /"ar (DEC)" = (1/2 " Γ AE Γ DM" )/(1/2 " Γ EC Γ DM " )
"ar (ADE)" /"ar (DEC)" = "AE" /"EC"
Now,
βBDE and βDEC are on the same base DE
and between the same parallel lines BC and DE.
β΄ ar (BDE) = ar (DEC)
Hence,
"ar (ADE)" /"ar (BDE)" = "ar (ADE)" /"ar (DEC)"
"AD" /"DB" = "AE" /"EC"
Hence Proved.

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!