Constructing With Angles (SAS And ASA)

We have seen how to construct triangles given all three side lengths. Now, we will explore constructing a triangle when two sides and one angle are known.

This is called the SAS (Side-Angle-Side) method.

Problem. Construct a triangle $ABC$ with $AB = 5\text{ cm}$, $AC = 4\text{ cm}$, and an included angle $\angle A = 45^\circ$.

Now, let's look at another common scenario: constructing a triangle when we know two angles and the side between them.

This is known as the ASA (Angle-Side-Angle) method.

Problem. Construct a triangle $ABC$ where the included side $AB = 5\text{ cm}$, $\angle A = 45^\circ$, and $\angle B = 80^\circ$.