Question

determining the included side
the included side between ∠a and ∠c is side
the included side between ∠a and ∠b is side
the included side between ∠c and ∠b is side
(image of triangle with vertices a, b, c)

Explanation:

Step1: Recall included side definition

The included side between two angles in a triangle is the side that is common to both angles (i.e., the side that forms the two angles with the other two sides). In triangle \(ABC\), the vertices are \(A\), \(B\), and \(C\).

Step2: Find included side for \(\angle A\) and \(\angle C\)

\(\angle A\) and \(\angle C\) meet at vertex \(A\) and \(C\), so the side between them is \(AC\) (since it's the side connecting \(A\) and \(C\), common to both angles).

Step3: Find included side for \(\angle A\) and \(\angle B\)

\(\angle A\) and \(\angle B\) meet at vertex \(A\) and \(B\), so the side between them is \(AB\) (connecting \(A\) and \(B\), common to both angles).

Step4: Find included side for \(\angle C\) and \(\angle B\)

\(\angle C\) and \(\angle B\) meet at vertex \(C\) and \(B\), so the side between them is \(BC\) (connecting \(B\) and \(C\), common to both angles).

Answer:

The included side between \(\angle A\) and \(\angle C\) is side \(AC\).
The included side between \(\angle A\) and \(\angle B\) is side \(AB\).
The included side between \(\angle C\) and \(\angle B\) is side \(BC\).