To create different triangles with two sides of length 4 cm and a 45° angle, we need to consider the different triangle types and the possible configurations of those two sides and the angle.
The main types of triangles we can consider are:
1. **Isosceles Triangle**: Two sides are equal, and the 45° angle is between them.
2. **Scalene Triangle**: All sides and angles are different. The two sides of length 4 cm are not equal to the third side, and the 45° angle can be at any vertex.
3. **Right Triangle**: One 90° angle. The 45° angle implies that the other non-right angles are also 45°, making it an isosceles right triangle.
For an isosceles triangle with two equal sides of 4 cm, the 45° angle must be the vertex angle. This will create one unique triangle.
For a scalene triangle, the 45° angle cannot be between the two sides of equal length, or it would be isosceles. So, the 45° angle must be at one of the other vertices, with the two 4 cm sides emanating from it at different angles. However, if the 45° angle is one of the base angles, there's still only one unique triangle you can draw because the other base angle is determined by the fact that triangle angles sum to 180°.
In a right triangle, since one angle is 90° and another is 45°, the third must also be 45°, which again yields an isosceles right triangle. There's only one such triangle that can be formed.