Question

in exercises 30 - 32, use the cube. 30. name three collinear points. 31. write an example of the three point postulate.

Explanation:

Step1: Recall collinear points definition

Collinear points lie on the same line.

Step2: Identify points on cube edges

On a cube, points on the same - edge are collinear. For example, points \(A\), \(E\), and \(J\) lie on the same edge of the cube.

Step3: Recall three - point postulate

The Three - Point Postulate states that through any three non - collinear points, there is exactly one plane. For non - collinear points on the cube, say \(A\), \(D\), \(H\). These three non - collinear points determine a plane (the bottom - face plane of the cube in this case).

Answer:

1. \(A\), \(E\), \(J\) (answers may vary, any three points on the same edge of the cube are correct)
2. Points \(A\), \(D\), \(H\) are non - collinear and they determine a plane (the bottom - face plane of the cube) (answers may vary, any three non - collinear points on the cube can be used to illustrate the postulate)