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ABē ABCD ACē ADē altitude angle arc CD base base and altitude BCē bisector bisects chord circle circle whose center circumference Computation cone construct cube determine diagonal diameter distance Draw drawn edge equal equally distant equidistant equilateral triangle faces feet Find the volume frustum Given Given isosceles Given planes given point half Hence hexagon hypotenuse inches inscribed intersecting joining lateral area locus medians meet middle point opposite parallel parallel planes parallelogram parallelopiped passes perimeter perpendicular plane plane MN prism projection Proof Prove Prove Proof pyramid radius ratio rectangle respectively right angles right triangle side similar Similarly sphere square straight line surface tangent third trapezoid triangle vertex
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 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.