are equal," growled Isosceles, wiping the jam off Tommy's face.

"So is my body," groaned Tommy, "unless it has been crushed out of shape by that horrid chair."

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Oh, it seems all right, but it would have served you right if it had been spoilt," grumbled Isosceles as he stuck Tommy's head on the top of his bruised body.

"His limbs are like me: none of their sides are alike," said Scalene in a plaintive voice as he collected the scattered arms and legs and fastened them on to the rest of Tommy.

Equilateral then clapped his cap on, and Tommy sat up and asked for more jam.

"You are a good-for-nothing boy," scolded his father.

"I'm very useful," contradicted Tommy, "for if it hadn't been for me people would never know how many different kinds of triangles there are.'

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Quite right, my pet," crooned his adoring mother, as she opened a fresh pot of jam for Tommy.

Now this is what Tommy had proved:

A Triangle is a figure bounded by three straight lines. A Triangle with all its sides equal is called an Equilateral Triangle. A Triangle with two sides equal is called an

Isosceles Triangle. A Triangle with no sides equal is called a Scaleǹe Triangle.

Your Geometry books will show you how to make each of these Triangles, and will also show you what a lot of other things you can do with them.

1. Join the letters in their right order, starting at A, and ending with I. Then join I to F. Count the number of figures in the kite after

you have drawn a face in it, using only circles and triangles. Colour it.

2. Make these triangles with sticks: Equilateral, Isosceles, Scalene.

3. Draw a straight line the length of your little finger.

With centre A and radius AB describe a circle.

With centre B and radius BA describe another circle, cutting the former circle in the points C and D.

Join AC, BC.

Rub out the circles. What figure have you left?

Measure each side of this triangle. You will find they are all the same length, so you have made an Equilateral Triangle.

Measure each angle in the triangle. You will find they are all equal, and if you add them together you will discover that they come to 180 degrees, or two right angles.

Draw a straight line 1 inch long. Measure 2 inches with your compasses, and taking it as a radius describe a circle from one point in your 1 inch line. With the same radius describe another circle from the other end of your one inch line.

Join the ends of your 1 inch line to the point where the circles cut. You will have made an

Isosceles Triangle. Measure its angles, and you will find there are altogether 180 degrees in it.

In describing triangles, it is only necessary to have a little bit of a circle (an arc), just to show the point where the two circles would meet.

Now see if you can describe an Isosceles Triangle, having each of the equal sides 1 inches long.

4. Name the different kinds of triangles in the picture of the Pointed-faced Man.

Colour his eyes brown, his mouth red, his face pink, and his hat green and yellow.

V

TO DESCRIBE AN EQUILATERAL TRIANGLE ON A GIVEN STRAIGHT

LINE

HERE is a Geometrical Proposition fully worked out. It is taken from Euclid's First Book, and it is the first Proposition.

Problem (Book I, Prop. 1).

To describe an Equilateral Triangle on a given straight line.

Given.

Let AB be the given straight line. Required. To describe an equilateral triangle on AB.

•Construction. With centre A and radius AB, describe an arc of a .

With centre B and radius BA describe another arc of a O cutting the former arc at the point C.