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acute adjacent altitude Auth base bisector bisects chord circle circumscribed common Compare Complete cone congruent Construct cylinder demonstration determine diagonal diameter difference dihedral distance divided division Draw drawn edges equal equidistant extended extremities faces figure Find formed four geometry given line given point greater Hence inches included inscribed intersect isosceles joining lateral area length less limit line parallel locus mean measure meet method oblique opposite parallel parallel planes parallelogram parallelopiped pass perimeter perpendicular placed plane polygon polyhedral polyhedron prism PROBLEM projection Proof proportional PROPOSITION Prove pyramid radii radius ratio rectangle regular polygon relation respectively right angle right triangle sect segment Show sides similar sphere spherical square straight line surface tangent THEOREM third triangle trihedral unit vertex vertices volume
Page 305 - If two polygons are similar, they can be divided into the same number of triangles, similar each to each, and similarly placed. 294. Theorem IX. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar.
Page 51 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 223 - ... indefinite length ; as CD. 12. The direction of the line AB means the direction from A toward B; of BA, the direction from B toward A.
Page 352 - If two triangles have the three sides of one equal respectively to the three sides of the other, the triangles are congruent, (sss) REMARK 1.
Page 302 - O'G O'A' X O'B' O'C' OA X OB X OC V' O'EX O'F O'G O'EX O'FX O'G QED 633. DEF. Similar polyhedrons are polyhedrons that have the same number of faces similar each to each and similarly placed, and have their homologous polyhedral angles equal.
Page 288 - The volume of any prism is equal to the product of its base by its altitude.
Page 290 - All these triangles meet in a point called the vertex. The perpendicular distance from the vertex to the plane of the base is the altitude or the height of the pyramid.
Page 361 - A zone is a portion of the surface of a sphere included between two parallel planes.