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Page 19 - ... 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.
Page 17 - 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.
Page 17 - 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.
Page 130 - Report on the work of the Bureau of Education for the natives of Alaska, 1911-12.
Page 18 - 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.
Page 38 - University of Maryland School of Medicine and College of Physicians and Surgeons, Baltimore.
Page 17 - Angles at a point. — If a straight line stands on another straight line, the sum of the two angles so formed is equal to two right angles; and the converse. If two straight lines intersect, the vertically opposite angles are equal. Parallel straight lines. — 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...
Page 18 - 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.
Page 191 - Scandinavian countries are so unique and contain so much of interest to all who are concerned in the preparation of young men and women for higher and better living and for more efficient citizenship that, although two or three former bulletins of this bureau have been devoted to a description of these schools and their work, I recommend that the manuscript transmitted herewith be published as a bulletin of the Bureau of Education for the purpose of giving a still more comprehensive account of the...
Page 18 - In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.