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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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.
Yes
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.
True
It can be. If two of the sides of a right triangle are the same length then it is an isosceles triangle