Wentworth's Plane and Solid Geometry · Book I, §§ 36–56 · Book 2: Book I: Rectilinear Figures
3. Lines, planes and the straight line
Goal: Your student can define straight, curved and broken lines, a plane, and equal and equivalent figures, and knows the postulates and axioms of the straight line.
You'll need
- The book, open to these pages
- A ruler (straightedge) and a pair of compasses
- Sharp pencil, eraser and plain paper (or a geometry notebook)
What's in the book
The first definitions of Book I (straight, curved and broken lines, plane surfaces, rectilinear figures, similar, equivalent and equal figures), then the postulates and axioms of the straight line and the idea of a segment.
The lesson, step by step
Warm up
Ask: What is the difference between an axiom and a postulate? What is the converse of a theorem?
Kinds of lines
Read §§ 36–38. Have your student draw a straight line, a curved line and a broken line, and label them.
A straight line is often called simply a line.
Planes and figures
Read §§ 39–43. The words similar, equivalent and equal are used all through the book. Draw two squares of different sizes (similar), a 2 × 8 rectangle and a 4 × 4 square (equivalent: same area), and two copies of one triangle (equal).
Postulates and axioms of the line
Read §§ 44–49 together:
A straight line can be drawn from one point to another.
A straight line can be produced indefinitely.
A straight line is the shortest line that can be drawn from one point to another.
Ask: Why can two straight lines cross in only one point? (§ 48: if they had two points in common they would be the same line.)
Segments
Read §§ 50–56. Draw a line, mark A, C and B on it, and show that AB = AC + CB. Mark off equal steps with the compasses to show a line "multiplied" by a number.
Wrap up
Your student gives the definitions of a straight line and a plane in their own words, then adds them to the notebook.