gmat prep geo
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1)
You know BD=BC given BCD is isocele.
You have AD and you want to make a link with BC.
Angle DBC=180-4x
Angle ABC=180-3x
Join both equations with that:
Angle ABC= Angle ABD + Angle DBC
180-3x=Angle ABD + 180-4x
Angle ABD=x
So Angle ABD=Angle BAD so ABD is an isocele triangle
And AD=BD=BC=6
2) does not give you information about the sides.
You know BD=BC given BCD is isocele.
You have AD and you want to make a link with BC.
Angle DBC=180-4x
Angle ABC=180-3x
Join both equations with that:
Angle ABC= Angle ABD + Angle DBC
180-3x=Angle ABD + 180-4x
Angle ABD=x
So Angle ABD=Angle BAD so ABD is an isocele triangle
And AD=BD=BC=6
2) does not give you information about the sides.