Second-year Mathematics for Secondary Schools

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University of Chicago Press, 1916 - Mathematics - 348 pages
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Page 305 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Page 8 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 342 - 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 243 - If two sides of one triangle are equal to two sides of another triangle...
Page 71 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.
Page 7 - If two parallel lines are cut by a transversal, the corresponding angles are equal.
Page 306 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.
Page 202 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 341 - I label the two new points e and/.' With the help of this figure he then proceeds to the usual proof of the theorem that the area of a parallelogram is equal to the product of the base by the altitude, establishing the equality of certain lines and angles and the congruence of the pair of triangles.
Page 199 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

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