draw another line, A E, outside the line A C, the angle E A B will be an OBTUSE ANGLE, because it is wider than a right angle.

Now we can again refer to the kite, and we shall soon be able to point out the different sorts of angles in it. Firstly, at the point C, where the long line DE bisects the line A B, you will see that there are four right angles meeting together, and I must tell you that if you want to know if the angles of any objects are right angles, put four of them together and see if they will all go close to each other. Take four of your lesson-books, and place them on the table, touching each other; you will find that there will be no space to spare between them, but that they will be quite close together, and this is because the corners of the four books are right angles.

But let us think of the other angles in the kite. Look at the bottom point, E, and you will at once see that it is a sharp point, and therefore it is an

ACUTE ANGLE.

You can test this (that is, you can try if it is true) in this way. Turn the book round so that the line E B is horizontal or flat, then you will see that the dotted line E H, and the line E B make a right angle, but that the line E A slants inward, and

thus the angle formed by the lines A E and E B is

an acute angle.

Next look at the line A D and the line D B in the upper part of the kite, and you will see at once that these two lines form an OBTUSE (or wide) ANGLE, for the lines ID and D A make a right angle, and it is clear that the line D B opens much further out. I have already told you that to cut a line into two equal parts is called "to bisect it," but we sometimes require to bisect an angle, and this shall be the subject of the next lesson.

TO BISECT AN ANGLE.

WHEN you have drawn your angle A (Fig. 21) mark on one of the lines a point, which I have called B, at any part you like; then mark on the other line the point C, but this requires a little more care, for C must be exactly the same distance from A on the one line that B is from A on the other; and you must try to get this quite correct before you proceed, or your work will turn out wrong in the end, and this will waste your time. You know that in doing a sum, if you have not been

careful to get the figures right in the first lines, the answer will be wrong, and this lesson must be done with just as much care.

B

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21

E

But to return to our figure. When you have marked the points B and C, mark the point D at any distance you like from B, and the point E at exactly the same distance from C that D is from B. Now you must test your drawing. You will remember that B and C were to be at the same distance from A, and therefore, as you have added equal lengths, BD and C E to them, the length from D to A ought to be exactly the same as from E to A. Examine if it is so. Well, we will believe that the lengths are quite right, and go on. Draw a line from B to E, and another from D to C; and these two lines will cross each other at the point F. Now,

if you draw a line from A to pass straight through F, it will bisect the angle.

You will see that the line E D, which forms the back-bone of the kite, bisects the angle at the bottom, and thus we have made a kite useful as well as amusing.

OF TRIANGLES.

Triangles are figures which have three sides; but still they are not all the same, for their exact shape depends on the length of each of the three lines. When all three sides are exactly the same, the figure is called an equilateral triangle, for the word e-qui-lat-e-ral means equal-sided.

At some time or other you shall learn to do all these figures with instruments called compasses and rules; but firstly I am going to teach you how to draw them by using your pencil only, and in this way you will soon get into the habit of seeing things in a very exact manner, which will be useful to you in a great many ways.

The bottom line, A B, of the triangle, Fig. 22, is called the BASE. Now, to draw an equilateral triangle, draw a per-pen-dic-u-lar at C, exactly in

the middle of the line A B.

On this per-pen

dic-u-lar mark a point, D, and when you have marked it look carefully at your work, and see whether the distances from D to B, and from D to A are the same as from A to B, and if these

lengths are exactly equal draw the lines which form the side of the triangle; but if you find that the distances from D to A and B are shorter than from A to B, you must move the point D higher up on the per-pen-dic-u-lar; if they are longer than A B you must bring D lower down.

You will see then that we have two things to