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University of Allahabad, 1909
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Seite 172 - If two triangles have two sides of the one equal to two sides of the other, each to each, and also the angles contained by those sides equal, the triangles are congruent.
Seite 175 - 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.
Seite 231 - 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.
Seite 172 - 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.
Seite 173 - The locus of a point which is equidistant from two fixed points is the perpendicular bisector of the straight line joining the two fixed points. The locus of a point which is equidistant from two intersecting straight lines consists of the pair of straight lines which bisect the angles between the two given lines.
Seite 232 - 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.
Seite 174 - The angle which an arc of a circle subtends at the centre is double that which it subtends at any point oil the remaining part of the circumference. Angles in the same segment of a circle are equal; and...
Seite 172 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Seite 233 - A ngles 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 lie on a circle. The angle in a semi-circle is a right angle, the angle in a segment greater than a semi-circle is less than a right angle, and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary ; and the converse.
Seite 52 - April, 1930. 2. Definitions: In this Act, unless there is anything repugnant in the subject or context: (a) "child...

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