Question

name the included angle for each pair of sides.

1. \\( \overline { p q } \\) and \\( \overline { p r } \\)
2. \\( \overline { r q } \\) and \\( \overline { p r } \\)
3. \\( \overline { p q } \\) and \\( \overline { r q } \\)

name the included side for each pair of angles.

1. \\( \angle p \\) and \\( \angle n \\)
2. \\( \angle n \\) and \\( \angle o \\)
3. \\( \angle d \\) and \\( \angle p \\)

Explanation:

Step1: Recall the definition of included angle

The included angle between two sides of a triangle is the angle formed by those two sides.
For \(\overline{PQ}\) and \(\overline{PR}\), the angle formed by them is \(\angle P\).

Step2: Apply the definition to the second pair

For \(\overline{RQ}\) and \(\overline{PR}\), the angle formed by them is \(\angle R\).

Step3: Analyze the third pair

For \(\overline{PQ}\) and \(\overline{RQ}\), the angle formed by them is \(\angle Q\).

Step4: Recall the definition of included side

The included side between two angles of a triangle is the side that is common to both angles.
For \(\angle P\) and \(\angle N\), assume the triangle has vertices \(P\), \(N\), \(D\) (from the first - part triangle). The side common to \(\angle P\) and \(\angle N\) is not applicable as per the first - part triangle (assuming proper vertex - matching). Wait, no, if we consider the first - part triangle with vertices (say \(P\), \(N\), \(D\)):
For \(\angle P\) and \(\angle N\), the included side is \(PN\).

Step5: For \(\angle N\) and \(\angle O\)

Assuming a triangle (if we consider the second - part triangle with vertices \(O\), \(Q\), \(R\) and first - part triangle vertices properly related). If we assume a combined or related triangle structure, the included side between \(\angle N\) and \(\angle O\) is \(NO\).

Step6: For \(\angle D\) and \(\angle P\)

The included side between \(\angle D\) and \(\angle P\) is \(DP\).

Answer:

1. \(\angle P\)
2. \(\angle R\)
3. \(\angle Q\)
4. \(PN\)
5. \(NO\)
6. \(DP\)