Ray's New Higher Arithmetic · Arts. 397–403 · Unit 28: Mensuration
119. Lines, angles, surfaces and polygons
Goal: Your student uses the book's names for lines, angles, plane figures, triangles and quadrilaterals.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
- A ruler
What's in the book
Chapter XXII, Mensuration: geometry and mensuration, kinds of lines, angles, surfaces and planes, polygons with pictures of regular polygons, kinds of triangles, and quadrilaterals and parallelograms.
The lesson, step by step
Warm-up
Ask your student to find a straight line, a curve, a right angle and a rectangle in the room.
The idea
Read:
Geometry is that branch of mathematics which treats of quantity having extension and form.
Mensuration is the application of Arithmetic to Geometry
A line is that which has length only.
A straight line is the shortest distance between two points.
Surfaces and polygons
Read:
A Plane is a surface such that any two points in it can be joined by a straight line which lies wholly in the surface.
The application of a straight-edge is the test of a plane.
A polygon is a portion of a plane inclosed by straight lines; the perimeter of a polygon is the whole boundary.
A polygon is regular when it has all its sides equal, and all its angles equal.
Triangles
Read:
A triangle is scalene when it has no equal sides; isosceles, when it has two equal sides; and equilateral, when its three sides are equal.
Have your student draw one of each.
Quadrilaterals
Read:
A Trapezoid is a quadrilateral having two and only two sides parallel.
A Parallelogram is a quadrilateral having two pairs of parallel sides.
A Rhombus is a parallelogram whose four sides are equal.
Note that in this book a trapezium has no parallel sides at all.
Wrap-up
Play a naming game: you describe a shape ("four equal sides, no right angle"), and your student names it (a rhombus).