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altitude angles are equal axis base called circle circumscribed common congruent considered construct containing corresponding cube cubic definitions denotes determine diagonal diameter diedral angles difference dimensions distance divided draw drawn element equal equilateral equivalent EXERCISES face angles figure Find the area Find the volume formed formula four frustum geometry given line given point greater Hence inches included inscribed intersection lateral area lateral edges length less locus lune measure meet opposite parallel planes parallelepiped parallelogram pass perimeter perpendicular plane Q polar pole polyedral angle polyedron polygon prism Problem projection Proof proportional prove pyramid radii radius ratio rectangular regular respectively right circular cone segment Show sides similar slant height solid sphere spherical polygon spherical triangle square straight line surface symmetric tangent tank tetraedron Theorem third total area triangular triedral vertex vertices zone
Page 434 - 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.
Page 439 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 319 - The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Let AD...
Page 395 - The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.
Page 294 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.
Page 292 - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane. Let AB, A'B', be parallel lines, and let n s' AB be perpendicular to the plane MN; then, A'B
Page 432 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 293 - The projection of a point upon a plane is the foot of the perpendicular from the point to the plane.