No.
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A triangle that has one right angle and is isosceles is called an isosceles right triangle.
An isosceles triangle can have a 90 degree angle, but doesn't necessarily. Similarly, a right triangle can be an isosceles triangle, but isn't necessarily.
An isosceles obtuse triangle is a triangle with 1 obtuse angle and only 2 congruent sides.
A triangle with two congruent sides is isosceles. A triangle with an angle of 104 degrees is obtuse. So you would have an obtuse isosceles triangle.
Only if the vertex angle being bisected is between the sides of equal length will the result be two congruent triangles.