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ABCD altitude approaches axis base bisector called centre chord circle circumference circumscribed coincide common cone construct contains corresponding cylinder diagonals diameter diedral angles difference distance divided draw drawn edges equal equilateral equivalent Exercise extremities faces figure Find formed four given given point given straight line GIVEN—the greater half Hence homologous included inscribed intersection lateral length less limit line joining locus mean measured meet method middle points parallel parallelogram pass perimeter perpendicular plane pole polyedron polygon prism PROBLEMS proportional PROPOSITION PROVE pyramid quadrilateral radii radius ratio rectangle regular respectively right angles right triangle segments sides similar sphere spherical square straight line surface tangent tetraedron THEOREM third triangle ABC unit vertex vertices volume
Side 36 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...
Side 321 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.
Side 211 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Side 42 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Side 385 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Side 144 - ... twice the product of one of these sides and the projection of the other side upon it.
Side 63 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Side 141 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.