• 3.22: The problem is telling us that the sides $DE$ and $BC$ of triangles $ADE$ and $ABC$ are parallel. Based on that, what can we say about the angles of triangle $ADE$ and $ABC$? Could you use that to show that $ADE$ is also an equilateral triangle?
• 3.23: You want to show that two angles in a triangle are equal if and only if the sides that are opposite to those two angles are equal.

What have you tried so far for 3.24, 3.25 and 3.30? Here are some hints:

• 3.24: try looking for some similar or congruent triangles.
• 3.25 and 3.30: remember the ratio of the sides of $45-45-90$ triangles is $1:1:\sqrt{2}$, and the ratio of the sides of $30-60-90$ triangles is $1:\sqrt{3}:2$.