Question

B

Answer 1

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