CalendarUniversity of Allahabad, 1907 |
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Page 223
... one equal to two angles of the other , each to each , and also one side of the one equal to the corresponding side of the other , the triangles are congruent . If two sides of a triangle are equal , the angles oppo- site to these sides ...
... one equal to two angles of the other , each to each , and also one side of the one equal to the corresponding side of the other , the triangles are congruent . If two sides of a triangle are equal , the angles oppo- site to these sides ...
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Popular passages
Page 180 - 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 223 - 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 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 -f 6 + c + ...) = ka + kb + kc + . .., (a-\- b)' = a2 +2ab + b2, (a — b)- = a2 — 2ab + b2, a2 — b2 = (a + b) (a — b).
Page 224 - 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 225 - 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.
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Page 64 - Colleges in the same neighbourhood, will not be injurious to the interests of education or discipline ; and (»') that the College rules fixing the fees (if any) to be paid by the students have not been so framed as to involve such competition with any existing College in the same neighbourhood as would be injurious to the interests of education.