Wentworth's Plane and Solid Geometry · Book I, §§ 57–80 · Book 2: Book I: Rectilinear Figures
4. Angles and how they are measured
Goal: Your student can name and draw right, straight, acute, obtuse, reflex, vertical, complementary and supplementary angles, and knows that a right angle is 90°.
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)
- A protractor
What's in the book
The plane angle and how angles are named, the postulate of superposition, adjacent, right, straight, acute, obtuse and reflex angles, the angle as a rotation, the perigon, vertical, complementary and supplementary angles, and the degree.
The lesson, step by step
Warm up
Ask: State the axiom about the shortest line between two points.
What an angle is
Read §§ 57–58.
The size of an angle depends upon the extent of opening of its sides, and not upon the length of its sides.
Draw two angles of the same opening, one with long sides and one with short. Which is bigger? (Neither.)
Equal by fitting
Read §§ 59–60. Two figures are equal if one can be placed on the other so they coincide. Trace an angle on thin paper and lay it on another to test them. This idea runs through the early proofs.
Kinds of angles
Read §§ 61–71. Your student draws and labels: adjacent angles, a right angle, a straight angle, an acute, an obtuse and a reflex angle.
Turning makes angles
Read §§ 72–78. Hold a pencil at a point and turn it: a quarter turn makes a right angle (90°), a half turn a straight angle (180°), a full turn a perigon (360°).
Then read the definitions of vertical, complementary and supplementary angles.
Quick practice
With the protractor: draw an angle of 35°. What is its complement? (55°.) Its supplement? (145°.) Draw two crossing lines and mark the two pairs of vertical angles.
Wrap up
Your student defines complementary and supplementary angles from memory and gives one example of each.