Yes
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An isosceles triangle has two equal sides and two equal angles. A right triangle is any triangle with one angle that is a right angle. A right triangle could also be an isosceles triangle, but an isosceles triangle will not always have a right angle.
A right triangle and an isosceles triangle have the fact that they are both triangles in common. A right triangle can also be an isosceles triangle.
In an isosceles triangle, two angles, and therefore sides (Base Angle Theorem), are congruent. This does not mean that all isosceles triangles are also right triangles - there is only one (45, 45, 90 triangle).
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It can be. If two of the sides of a right triangle are the same length then it is an isosceles triangle