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ABCD altitude base bisected bisectors called chord circle circumference circumscribed common cone congruent considered construct converse convex COROLLARIES corresponding DEFINITIONS described determined diagonals diameter difference dihedral angle distance divided draw drawn edges equal equilateral EXERCISES faces figure Find four frustum geometry given given line given point greater half Hence included inscribed intersection joining lateral less locus mean measure meet Note opposite sides parallel parallelogram pass perigon perimeter perpendicular placed plane polygon Post prism Problem produced Proof proportional prove pyramid quadrilateral radius ratio rectangle regular respectively right angle segments sides similar Similarly solid solution space sphere spherical square step straight line student Suppose surface symmetric tangent Theorem transverse triangle true vertex vertices volume zero
Side 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Side 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...
Side 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Side 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.
Side 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.
Side 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.
Side 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.
Side 94 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.