Key to the Exercises in Wells's New Geometry

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D.C.Heath & Company, 1909
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Page 93 - 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 93 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their intersection, is perpendicular to the other.
Page 83 - A straight line is perpendicular to a plane when it is perpendicular to every straight line drawn in the plane through its foot; that is, through the point in which it meets the plane.
Page 87 - If two angles not in the same plane have their sides parallel and extending in the same direction, they are equal, and their planes are parallel. Given ABAC and B'A'C" in planes MN and PQ, respectively, with AB and AC II respectively to A'B' and AC', and extending in the same direction. To Prove Z BAC = Z B'A'C', and MN II PQ. Proof. Lay off AB = A'B' and AC = A'C', and draw lines AA, BB', CC', BC, and B'C'.
Page 100 - DE'F, and consequently symmetrical with DEF. PROPOSITION XIII.—THEOREM. 55. Two triangles on the same sphere are either equal or symmetrical, when a side and two adjacent angles of one are equal respectively to a side and two adjacent angles of the other.
Page 108 - If a pyramid is cut by a plane parallel to its base, the area of the section is to the area of the base as the square of its distance from the vertex is to the square of the altitude of the pyramid.
Page 90 - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.
Page 86 - If a straight line is parallel to a plane, the intersection of the plane with any plane passed through the given line is parallel to that line.
Page 86 - Only one straight line can be drawn through a given point parallel to a given straight line.
Page 119 - H, whatever be the number of sides : hence, the convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude.

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