Now mark any four points on your paper so that no three of them are on one line. Label them A, B, C, D. Draw all possible lines going through pairs of these points. How many lines do you get? Name them. How many angles can you name using A, B, C, D? Write them all down, and mark each of them with a curve as in Fig. 2.9.
Lines through pairs of points: Six lines can be drawn through pairs of four non-collinear points. Names of lines: AB, AC, AD, BC, BD, CD
Angles formed: Number of angles: 12 These angles are formed at each of the six intersection points where lines cross. At each intersection point, two angles are formed (one on each side of the crossing lines).
Explanation
The chapter explains that any two points determine a unique line. With four points, we can choose pairs in 4C2 = 6 ways, giving six lines. These lines intersect at various points, creating multiple angles. Students should draw all six lines connecting the four points and identify all angles formed at intersection points. The angles should be named using three-letter notation with the vertex as the middle letter.
Solution Steps
Mark four points A, B, C, D on paper such that no three of them are on one line.
Draw all possible lines going through pairs of these points.
Count and name the lines: AB, AC, AD, BC, BD, CD (6 lines total).
Identify all angles formed at intersection points where lines cross.
Count the angles: 12 angles formed at six intersection points.