

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Theorems
Theorem 6.2 - Converse of Basic Proportionality Theorem
Theorem 6.3
AA Similarity Criteria
Theorem 6.4 Important
Theorem 6.5
Theorem 6.6 Important Deleted for CBSE Board 2024 Exams
Theorem 6.7 Important Deleted for CBSE Board 2024 Exams
Theorem 6.8 Important Deleted for CBSE Board 2024 Exams
Theorem 6.9 Deleted for CBSE Board 2024 Exams
Last updated at May 29, 2023 by Teachoo
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.