EFGH is a parallelogram.EI bisects angle E and GJ bisects angle G. I lies on GH and J lies on EF. Show that EI is paralĺel GJ and EJGI is a parallelogram
Answers
EI ║ GJ and EJGI is parallelogram if EFGH is a parallelogram.EI bisects angle E and GJ bisects angle G. I lies on GH and J lies on EF.
Step-by-step explanation:
EFGH is parallelogram
=> ∠ E = ∠G ( opposite angles equal)
& ∠E + ∠F = 180° ( sum of adjacent angle)
EI bisects angle E
=> ∠FEI = ∠E/2
=> ∠JEI = ∠E/2
∠EJG = ∠JGF + ∠F ( Exterior angle of triangle = sum of opposite interior angles)
∠JGF = ∠G/2 ( as GJ Bisect ∠G)
=> ∠JGF = ∠E/2 ( as ∠ E = ∠G)
∠EJG = ∠E/2 + ∠F
now adding ∠JEI & ∠EJG
∠JEI + ∠EJG = ∠E/2 + ∠E/2 + ∠F
=> ∠JEI + ∠EJG = ∠E + ∠F
=> ∠JEI + ∠EJG = 180°
=> EI ║ GJ
QED
Proved
EJ ║ GI ( as I lies on GH and J lies on EF and GH ║ EF)
Hence EJGI is parallelogram
Learn more:
in the following figure ABCD is a parallelogram prove that AP bisects ...
https://brainly.in/question/14040520
BY bisects angle b of triangle ABC. Prove that BZYX is a rhombus ...
https://brainly.in/question/13770065
Answer:
Refer to the attachment
It's my guarantee that this is correct
Hope it will help you
Have a nice day
thanks
