How many different triangles are there, which satisfy the following properties:

- The triangle is isosceles.
- The triangle has an angle which is $40 ^ \circ$ .
- The triangle has a side of length 40.

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Details and assumptions
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2 triangles are different if they are not congruent.

Rotations, reflections and translations of a triangle are considered the same.

The answer is 4.

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From the first and second conditions, the triangle must either be $40^\circ - 40^ \circ - 100^ \circ$ or $40^\circ - 70^ \circ - 70^ \circ$ .

To satisfy the third condition, either the equal sides, or the base of the triangle must be equal to 40. This gives $2 \times 2 = 4$ different triangles which satisfy the conditions.