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ABCD altitude base becomes bisected bisectors called chord circle circumference common cone congruent considered construct converse convex COROLLARIES corresponding DEFINITIONS determined diagonals diameter distance divided draw drawn edges equal equal angles equidistant equilateral EXERCISES faces figure Find four geometry given line given point greater half Hence included inscribed interior angles intersection isosceles joining lateral less locus mean measure meet mid-points Note opposite sides parallel parallelogram passes perpendicular placed plane polygon Post Problem produced Proof proportional prove pyramid quadrilateral radius ratio rectangle regular respectively right angle segments sides similar Similarly solution space sphere spherical square step straight angle straight line student suggested Suppose surface symmetric tangent Theorem transversal triangle true vertex vertices volume zero
Page 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Page 295 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 37 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 159 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 225 - Theorem. If each of two intersecting planes is perpendicular to a third plane, their line of intersection is also perpendicular to that plane. Given two planes, Q, R, intersecting in OP, and each perpendicular to plane M. To prove that OP _L M.
Page 265 - A Plane Surface, or a Plane, is a surface in which if any two points are taken, the straight line which joins these points will lie wholly in the surface.
Page 94 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.