(Note: Figure not drawn to scale)
Is triangle ABC isosceles?
(1) Angle ABC is not equal to Angle ACB
(2) AB=2BC
Is triangle ABC isosceles?
(1) Angle ABC is not equal to Angle ACB
(2) AB=2BC
1. Angle ABC is not equal to angle ACB. However, angle ABC may/may not be equal to angle BAC. So insufficient information to determine whether triangle ABC is isosceles.
2. Triangle rule: AB-BC<AC<AB+BC (why AB- BC, not BC - AB? Because AB>BC as given above)
BC<AC<3BC. From the range of value of AC, AC can be equal to, less than,more than AB ( or 2BC). Hence triangle ABC can not be determine to be an isosceles triangle.
1&2. Imagine we draw a circle in which triangle ABC is inscribed. Angle ABC is not equal to angle ACB, hence chord AC is not equal to chord AB. Now we get those conditions:
BC<AC< 3BC (from 2. above)
BC < AB ( AB = 2BC)
AC is not equal to AB.
Then AB,BC,AC are different from each other. Thus, triangle ABC can not be an isosceles triangle. My answer is C.
