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University of Allahabad, 1921
 

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Page 255 - 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 255 - 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.
Page 44 - 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...
Page 256 - 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.
Page 257 - 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.
Page 258 - 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 254 - A. Bisection of angles and of straight lines. Construction of perpendiculars to straight lines. Construction of an angle equal to a given angle. Construction of parallels to a given straight line. Simple cases of the construction from sufficient data of triangles and quadrilaterals. Division of straight lines into a given number of equal parts or into parts in any given proportions.
Page 258 - ... angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary ; and the converse. If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments. If two chords of a circle intersect either inside or outside the circle, the rectangle contained by the parts of the one is equal to the rectangle contained by the parts of the other.
Page 253 - Schedule B, together with questions upon these theorems, easy deductions from them, and arithmetical illustrations. Any proof of a Proposition will be accepted which appears to the Examiners to form part of a systematic treatment of the subject...
Page 255 - If two triangles have the three sides of the one equal to the three sides of SH 19 the other, each to each, the triangles are congruent.

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