Wentworth's Plane and Solid Geometry · Book II, §§ 216–234 · Book 3: Book II: The Circle
22. The circle: definitions
Goal: Your student can define and draw a circle, radius, diameter, secant, tangent, arc, chord, segment, sector, central and inscribed angles, and inscribed and circumscribed figures.
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 definitions at the start of Book II, The Circle, with the postulate that a circumference can be described from any centre with any radius.
The lesson, step by step
Warm up
Ask: What does it mean for a point to be equidistant from two points? Where are all such points?
The circle
Read §§ 216–218.
A circle is a portion of a plane bounded by a curved line, all points of which are equally distant from a point within called the centre.
Note that in this book the circle is the region; its edge is the circumference.
Draw and label
With the compasses, your student draws a large circle and adds, labeling each: a radius, a diameter, a chord, a secant, a tangent, an arc, a segment, a sector and a quadrant (§§ 219–228).
Angles in a circle
Read §§ 229–230. Add a central angle and an inscribed angle to the drawing.
Inscribed and circumscribed
Read §§ 231–234. Draw a triangle with all three corners on a circle (inscribed in it), and a circle touching all four sides of a square (inscribed in the square).
Wrap up
Point at parts of the drawing and ask for the name. Then ask for the difference between a chord and a secant.