1. (10 points) If two sides of the first triangle are respectively equal to two sides of the second triangle and the angle opposite one of these sides in the first triangle is equal to the angle opposite the corresponding equal side in the second triangle, then these triangles

a) are equal

b) are not equal

c) may be equal, or may not be equal

2) may have equal areas
Answer: c) and d).

Solution:

![](https://cdn.mathpix.com/cropped/2024_05_06_c45e0ad95d640fb17364g-2.jpg?height=321&width=709&top_left_y=1370&top_left_x=662)

The triangles mentioned in the problem can obviously be equal, for example, if they are equilateral. At the same time, equal triangles have equal areas, so answer option d) fits us.

Triangles $ABC$ and $ABC'$, shown in the figure, satisfy the condition but are obviously not equal ( $\omega$ - a circle centered at point $B$ ). Therefore, the second correct answer option is c).