The Bombay University Calendar, Volume 1

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Page 62 - 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 62 - 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 69 - 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 64 - 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...
Page 20 - Bombay for the purpose of ascertaining, by means of examination, the persons who have acquired proficiency in different branches of Literature, Science, and Art, and of rewarding them by Academical Degrees as evidence of their respective attainments, and marks of honour proportioned thereunto...
Page 64 - 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.
Page 63 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent If two sidus of a triangle are unequal, the greater side has the greater angle opposite to it; and the converse.
Page 64 - 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.
Page 63 - 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.
Page 63 - If two sides of a triangle are unequal, the greater side has the greater angle opposite to it ; and the converse. 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. 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...

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