Plane geometry (Google eBook)

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H. Holt and company, 1915 - History - 223 pages
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Page 205 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 96 - The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to one-half the length of the third side.
Page 65 - 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 186 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 82 - ... the angle opposite the third side of the first triangle is greater than the angle opposite the third side of the second.
Page 181 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 170 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 185 - 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 158 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 148 - 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.

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