Prove: Angle DAB Bisector when Given Parallelogram ABCD, Cyc. Quadrilateral BCED

  • Context: Graduate 
  • Thread starter Thread starter mathwizarddud
  • Start date Start date
  • Tags Tags
    Geometry Olympiad
Click For Summary
SUMMARY

The discussion focuses on proving that line l, which intersects segment DC at point F and line BC at point G, acts as the bisector of angle DAB in the context of parallelogram ABCD and cyclic quadrilateral BCED. Given the condition EF = EG = EC, the geometric properties of the figures allow for the conclusion that line l bisects angle DAB definitively. A visual representation is requested to aid in understanding the proof, emphasizing the importance of geometric constructions in such proofs.

PREREQUISITES
  • Understanding of basic geometric properties of parallelograms
  • Knowledge of cyclic quadrilaterals and their properties
  • Familiarity with angle bisectors and their geometric significance
  • Ability to construct geometric diagrams for visual proof
NEXT STEPS
  • Study the properties of cyclic quadrilaterals in depth
  • Learn about angle bisector theorems and their applications
  • Explore geometric proof techniques, particularly in parallelograms
  • Practice constructing geometric figures to visualize proofs
USEFUL FOR

Students of geometry, mathematics educators, and anyone interested in advanced geometric proofs and constructions.

mathwizarddud
Messages
25
Reaction score
0
Consider five points A, B, C, D and E such that ABCD is a parallelogram and BCED is a
cyclic quadrilateral. Let l be a line passing through A. Suppose that l intersects the interior
of the segment DC at F and intersects line BC at G. Suppose also that EF = EG = EC.
Prove that l is the bisector of angle DAB.
 
Mathematics news on Phys.org
Can you give a drawing? ( I'm a bit lazy )
 

Similar threads

Graduate Fun math problem from IMO 2007
  • · Replies 7 ·
Replies
7
Views
2K
Proving the Bisectors of a Quadrilateral Bisect Each Other
  • · Replies 3 ·
Replies
3
Views
7K
Graduate What Does Mathematical Sameness Mean?
  • · Replies 7 ·
Replies
7
Views
3K