Wentworth's Plane and Solid Geometry · Book II, Exs. 178–207 · Book 3: Book II: The Circle
38. Constructing triangles and squares from given parts
Goal: Your student constructs triangles, right triangles and squares from given parts, using analysis.
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
Pages 131–132: construction exercises 178–207 for isosceles, right and general triangles and for squares.
The lesson, step by step
Warm up
Ask: What are the four parts of the solution of a problem?
Warm-up constructions
Your student does two quick ones:
Ex. 178. To construct an equilateral triangle, having given the radius of the circumscribed circle.
Ex. 183. The hypotenuse and one leg.
(Ex. 183 is a right triangle; draw the hypotenuse as a diameter.)
Analysis first
Choose one harder problem, such as Ex. 192 or Ex. 195, and before constructing anything, sketch the finished figure and ask: "What is known? What can I build first?"
Construct and check
Construct it carefully, then measure to check that the given parts came out right.
Squares
Ex. 205. The diagonal.
Construct a square, given its diagonal. Then try Ex. 206, using the book's hint.
Wrap up
Your student explains the analysis of one problem in words, without the drawing.
Answers to the book's problems
Ex. 178: draw the circle and step off the radius six times around it; join alternate points (§ 469 later gives the proof). Ex. 183: draw a semicircle on the hypotenuse; from one end, with radius equal to the leg, cut the arc; the angle at the cut is right (§ 290). Ex. 205: draw the diagonal, its perpendicular bisector, and a circle on the diagonal as diameter; the four points are the vertices.
Worked out for this site from the scan. If a number in your copy differs, trust the book.