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Σελίδα 383 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 304 - The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference. Angles in the same segment of a circle are equal; and, if the line joining two points subtends equal angles at two other points on the same side of it, the four points He on a circle.
Σελίδα 386 - ... and the converse. If two triangles are equiangular their corresponding sides are proportional ; and the converse. If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 48 - The school board shall be a body corporate, by the name of the school board of the district to which they belong, having a perpetual succession and a common seal, with power to acquire and hold land for the purposes of this Act without any licence in mortmain...
Σελίδα 385 - If a straight line touch a circle, and from the point of contact a chord...
Σελίδα 224 - Areas Parallelograms on the same or equal bases and of the same altitude are equal in area. Triangles on the same or equal bases and of the same altitude are equal in area. Equal triangles on the same or equal bases are of the same altitude. Illustrations and explanations of the geometrical theorems corresponding to the following algebraical identities : k (a + b + c + ...) = ka + kb + kc + ..., The square on a side of a...
Σελίδα 303 - The opposite sides and angles of a parallelogram are equal, each diagonal bisects the parallelogram, and the diagonals bisect one another. If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.
Σελίδα 225 - The square on a side of a triangle is greater than, equal to, or less than, the sum of the squares on the other two sides, according as the angle contained by those sides is obtuse, right or acute. The difference in the cases of inequality is twice the rectangle contained by one of the two sides and the projection on it of the other.
Σελίδα 223 - When a straight line cuts two other straight lines, if (i) a pair of alternate angles are equal, or (ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles, then the two straight lines are parallel ; and the converse. Straight lines which are parallel to the same straight line are parallel to one another.