Examination Questions in Mathematics: Third Series, 1911-1915

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Ginn and Company, 1915 - Mathematics - 60 pages
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Page 47 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 46 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180 and less than 540. (gr). If A'B'C' is the polar triangle of ABC...
Page 25 - Three men, A, B, and C, can do a piece of work in 18, 24, and 36 hours, respectively.
Page 36 - If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar.
Page 38 - It follows from 259 that if through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 46 - The areas of two similar triangles are to each other as the squares of any two homologous sides.
Page 46 - If from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other secant and its external segment.
Page 44 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Page 36 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it. c Hyp. In A abc, p is the projection of b upon c, and the angle opposite a is obtuse. To prove a. = V + c2 + 2cp. Proof. a2 = K
Page 36 - Two triangles are congruent if the three sides of the one are equal, respectively, to the three sides of the other.

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