Q. What is this?  A. An equi-lateral triangle.  Q. Why is it called equi-lateral?  A. Because its sides are all equal.  Q. How many sides has it?  A. Three sides.  Q. How many angles has it?  A. Three angles.  Q. What do you mean by angles?  A. The space between two right lines, drawn gradually nearer to each other, till they meet in a point.  Q. And what do you call the point where the two lines meet?  A. The angular point.  Q. Tell me why you call it a tri-angle.  A. We call it a tri-angle because it has three angles.  Q. What do you mean by equal?  A. When the three sides are of the same length.  Q. Have you any thing else to observe upon this?  A. Yes, all its angles are acute.

Isoceles Triangle.

Q. What is this?  A. An acute-angled isoceles triangle.  Q. What does acute mean?  A. When the angles are sharp.  Q. Why is it called an isoceles triangle?  A. Because only two of its sides are equal.  Q. How many sides has it?  A. Three, the same as the other.  Q. Are there any other kind of isoceles triangles?  A. Yes, there are right-angled and obtuse-angled.

[Here the other triangles are to be shewn, and the master must explain to the children the meaning of right-angled and obtuse-angled.]

Scalene Triangle.

Q. What is this?  A. An acute-angled scalene triangle.  Q. Why is it called an acute-angled scalene triangle?  A. Because all its angles are acute, and its sides are not equal.  Q. Why is it called scalene?  A. Because it has all its sides unequal.  Q. Are there any other kind of scalene triangles?  A. Yes, there is a right-angled scalene triangle, which has one right angle.  Q. What else?  A. An obtuse-angled scalene triangle, which has one obtuse angle.  Q. Can an acute triangle be an equi-lateral triangle?  A. Yes, it may be equilateral, isoceles, or scalene.  Q. Can a right-angled triangle, or an obtuse-angled triangle, be an equilateral?  A. No; it must be either an isoceles or a scalene triangle.

Square.

Q. What is this?  A. A square.  Q. Why is it called a square?  A. Because all its angles are right angles, and its sides are equal.  Q. How many angles has it?  A. Four angles.  Q. What would it make if we draw a line from one angle to the opposite one?  A. Two right-angled isoceles triangles.  Q. What would you call the line that we drew from one angle to the other?  A. A diagonal.  Q. Suppose we draw another line from the other two angles.  A. Then it would make four triangles.

Pent-agon.

Q. What is this?  A. A regular pentagon.  Q. Why is it called a pentagon?  A. Because it has five sides and five angles.  Q. Why is it called regular?  A. Because its sides and angles are equal.  Q. What does pentagon mean?  A. A five-sided figure.  Q. Are there any other kinds of pentagons?  A. Yes, irregular pentagons?  Q. What does irregular mean?  A. When the sides and angles are not equal.

Hex-agon.