Given
Segments AB, CD ,and EF intersect at point O.
points A, E, C and points B, F, D are collinear
AO ≅ OB
, CO ≅ OD
Prove that
AE ≅ BF
To proof
As given in the question
points A, E, C and points B, F, D are collinear
Collinear points
These are the points lie in the single striaght line.
this shows points A, E, C and points B, F, D are lie in the single striaght line.
As given in the question
AO ≅ OB , CO ≅ OD
In ΔAOC and ΔBOD
AO ≅ OB
∠AOC = ∠ BOD ( Vertically opposite angle )
CO ≅ OD
ΔAOC ≅ Δ BOD
By using the SAS congurence property
∠CAO = ∠OBD
( By corresponding sides of the congurent triangle )
In ΔAOE and Δ BOF
∠OAE = ∠OBF ( As proof above )
AO = OB
∠AOE = ∠BOF ( Vertically opposite angle )
ΔAOE =Δ BOF
By using the ASA congurence property
AE ≅ BF
( By corresponding sides of the congurent triangle )
Hence proved
