4. а) [3] Can a square be cut into 4 isosceles triangles, none of which are equal? б) [3] Can an equilateral triangle be cut into 4 isosceles triangles, none of which are equal?

Vladimir Rastorguev

Answers: yes in both parts.
Solution. See figures. On the left figure, we first draw the angle bisector $A K$ of angle $B A C$, and then reflect point $B$ over $A K$ to obtain point $E$.
![](https://cdn.mathpix.com/cropped/2024_05_06_7266a76055d1b1da7f8dg-2.jpg?height=398&width=1010&top_left_y=560&top_left_x=642)