Question

Name two different ways to construct congruent angles

Answer 1

A first way is considering opposite angles:

• Pick a point, $O$
• Draw two rays $r,s$ starting from $O$
• Let $\alpha$ be the angle between $r$ and $s$
• Elongate both $r$ and $s$ with respect to $O$ to obtain the rays $r'$ and $s'$
• The angle between $r'$ and $s'$ is also $\alpha$

Alternatively, you can start with a given angle, and then draw its bisector. By definition, the bisector cuts a given angle in two equal parts, so you divide an angle $\alpha$ in two parts, both measuring $\frac{\alpha}{2}$