In quadrilateral ABCD, diagonals AC and BD intersect at E such that

         AE:EC=BE:ED

Show that ABCD is a parallelogram.
in Geometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

 

In  triangles ABE and CDE,

AE/EC = BE/ED (Because AE:EC=BE:ED)                                                                                                        So triangles ABC and APQ are equiangular.

Then angles BAE = DCE, So AB//DC (Becasue angles BAE = DCE are alternate angles and they are equal)

 

Also in  triangles ADE and BCE,

AE/EC = BE/ED (Because AE:EC=BE:ED)                                                                                                        So triangles ADE and BCE are equiangular.

Then angles CBE = ADE, So AD//BC (Becasue angles CBE = ADE are alternate angles and they are equal)

So ABCD is a parallelogram (since pairs of opposite sides are parallel)

by Level 2 User (1.7k points)

Related questions

1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,240 questions
90,465 answers
2,120 comments
78,597 users