Any two angles of a triangle are together less than two right angles. If two sides of a triangle are unequal, the angle subtended by the greater side is greater than the angle subtended by the less. If two angles of a triangle are unequal, the side opposite to or subtending the greater angle is greater than the side opposite the less angle. A B PROP. XX. THEOR. Any two sides of a triangle are together greater than the third side. B COR.-Hence the difference between any two sides of a triangle is less than the third side. If from any point within a triangle straight lines be drawn to the extremities of one side, these lines must be together less than the other two sides, but must contain a greater angle. A B PROP. XXII. PROB. To construct a triangle having its sides equal to three given straight lines, of which any two are together greater than the third. L PROP. XXIII. PROB. At a given point in a given straight line, to make an angle equal to a given rectilinear angle. PROP. XXIV. THEOR. If two triangles have two sides of the one respectively equal to two sides of the other, but the angles contained by those sides unequal, their bases also must be unequal; and that is the greater base which subtends the greater angle. D B4 PROP. XXV. THEOR. If two triangles have two sides of the one respectively equal to two sides of the other, but their bases unequal, the angle subtended by the greater base of the one, must be greater than the angle subtended by the less base of the other. да E |