Plane Geometry

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Century Company, 1916 - Geometry, Modern - 276 pages

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Page 31 - If two triangles have two sides of one equal respectively to two sides of the other...
Page 187 - 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 72 - A line drawn through the mid-points of two sides of a triangle is parallel to the third side.
Page 40 - Euclid, eg first asserts and proves, that the exterior angle of a triangle is greater than either of the interior opposite angles...
Page 107 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 187 - ... have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 133 - The sum of the angles of a triangle is equal to a straight angle.
Page 164 - The locus of a point at a given distance from a given point is the circumference described from the point with the
Page 78 - The lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Page 186 - A line drawn from the vertex of the right angle of a right triangle to the middle point of the hypotenuse divides the triangle into two isosceles triangles.

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