Remember we can give you better hints if you tell us a bit about what you have tried and how you got stuck in each of the problems.

Here are some hints:

3.22: Remember that the interior angles of a triangle add up to $180^\circ$

3.23: An isosceles triangle has two equal angles (opposite to the equal sides). Use this to find the angle measure of the other two angles in $\triangle AFJ$.

3.24: (i) Let $ABC$ be a triangle with $\angle A = \angle B$. Draw the angle bisector $\overline{CD}$ of $\angle C$ and prove $\triangle CAD \cong \triangle CBD$. (ii) Assuming now $AC = BC$ use a similar method to show that $\angle A = \angle B$.

3.25: What kind of triangle is $\triangle ABC$? What about $\triangle CBD$?

3.26: Compare to Example 3.10.

3.27: Use repeatedly the fact that the interior angles of a triangle add up to $180^\circ$ to find missing angles in the diagram. Start with $\triangle ABC$.

3.28: Compare to what was done for Example 3.5

3.29: Draw two of the perpendicular bisectors of a triangle. Use congruent triangles to show that the point where these intersect is equidistant to the three vertices of the triangle. From the point where they intersect draw a perpendicular line to the third side of the triangle. Show that the point where this line intersects the side of the triangle is the midpoint of that side.

3.30: Use the fact that the interior angles of a triangle add up to $180^\circ$ and that isosceles triangles have two equal angles (opposite to the sides that are equal).