Page:First six books of the elements of Euclid 1847 Byrne.djvu/14

angled triangle, and expreſs ſome of its properties both by colours and the method generally employed.

Some of the properties of the right angled triangle ABC, expreſſed by the method generally employed.

1. The angle BAC, together with the angles BCA and ABC are equal to two right angles, or twice the angle ABC.
2. The angle CAB added to the angle ACB will be equal to the angle ABC.
3. The angle ABC is greater than either of the angles BAC or BCA.
4. The angle BCA or the angle CAB is leſs than the angle ABC.
5. If from the angle ABC, there be taken the angle BAC, the remainder will be equal to the angle ACB.
6. The ſquare of AC is equal to the ſum of the ſquares of AB and BC.

The ſame properties expreſſed by colouring the different parts.

1. + + = 2 = .

That is, the red angle added to the yellow angle added to the blue angle, equal twice the yellow angle, equal two right angles.

2. + = .

Or in words, the red angle added to the blue angle, equal the yellow angle.

3. > or > .

The yellow angle is greater than either the red or blue angle.