In figure,AB is perpendicular to AE,BC is perpendicular to AB,BE=DE and angle AED=120, find: (a) EDC (b)DEC (c)Hence prove that EDC is an eq. triangle?
Dear Student,
Please find below the solution to the asked query:
Given : AED = 120 , AB is perpendicular on AE , So BAE = 90 and BC perpendicular to AB , So ABD = 90
From angle sum property of quadrilateral we get in quadrilateral ABDE :
BAE + AED + EDB + ABD = 360 , Substitute given values we get
90 + 120 + EDB + 90 = 360 ,
300 + EDB = 360 ,
EDB = 60
And
EDB = EDC = 60 ( Same angle ) ( Ans )
Also given DE = CE so from base angle theorem we get
EDC = ECD = 60
And from angle sum property of triangle we get in triangle EDC ,
EDC + ECD + DEC = 180 ,
60 + 60 + DEC = 180 ,
120 + DEC = 180 ,
DEC = 60 ( Ans )
Here we can see that all angles in triangle EDC are at 60 , SO we can say that triangle EDC is a equilateral triangle . ( Hence proved )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
RegardsE
Please find below the solution to the asked query:
Given : AED = 120 , AB is perpendicular on AE , So BAE = 90 and BC perpendicular to AB , So ABD = 90
From angle sum property of quadrilateral we get in quadrilateral ABDE :
BAE + AED + EDB + ABD = 360 , Substitute given values we get
90 + 120 + EDB + 90 = 360 ,
300 + EDB = 360 ,
EDB = 60
And
EDB = EDC = 60 ( Same angle ) ( Ans )
Also given DE = CE so from base angle theorem we get
EDC = ECD = 60
And from angle sum property of triangle we get in triangle EDC ,
EDC + ECD + DEC = 180 ,
60 + 60 + DEC = 180 ,
120 + DEC = 180 ,
DEC = 60 ( Ans )
Here we can see that all angles in triangle EDC are at 60 , SO we can say that triangle EDC is a equilateral triangle . ( Hence proved )
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
RegardsE