Two of the angles are the same. What shapes are possible?
To determine which shapes are possible when two angles are the same, we need to consider the properties of angles in different geometric shapes. Here are some possibilities:
1. Square: In a square, all angles are 90 degrees, so if two angles are the same, they must both be 90 degrees. Therefore, a square is a possible shape.
2. Rectangle: In a rectangle, opposite angles are equal, so if two angles are the same, they could be either two adjacent angles or two opposite angles. Therefore, a rectangle is another possible shape.
3. Parallelogram: In a parallelogram, opposite angles are equal. Hence, if two angles are the same, they could be either two adjacent angles or two opposite angles. Therefore, a parallelogram is another possible shape.
4. Rhombus: In a rhombus, all sides are equal, but opposite angles are not necessarily equal. However, if two angles are the same, the rhombus must be a square.
5. Isosceles Trapezoid: In an isosceles trapezoid, two opposite angles are equal, so if two angles are the same, they could be two adjacent angles or two opposite angles. Therefore, an isosceles trapezoid is another possible shape.
Remember, these are just a few examples of shapes where two angles could be the same. There are many other possibilities depending on the specific conditions and properties of the angles in a given shape.