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acute angle altitude h angle formed Angle Sine angles are equal bisect circle circumference congruent Corollary corresponding cube diameter dicular dihedral angle distance drawn equal altitudes equal spheres equilateral EXERCISES face angles Find the volume formula frustum gent Chord Arc given line given point Hence HINT hypotenuse inscribed intersection isosceles lateral area lateral edges length lines are parallel locus lune whose angle measured number of sides parallel planes parallelogram perimeter perpen perpendicular to MN plane angles Plane Geometry plane MN plane perpendicular points equidistant polar triangle pole prove radii radius ratio rectangular parallelepiped regular polygons regular polyhedron regular pyramid respectively right angles right prism right section right triangle segment Show similar slant height spherical degrees spherical excess spherical polygon spherical triangle square straight line surface tangent tetrahedron Theorem VII triangular prisms triangular pyramids trihedral truncated prism unequal V-ABC vertex vertices
Page xxxv - If two triangles have two sides of the one equal to two sides of the...
Page 224 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Page 303 - 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 258 - Aa, and let k be one of those parts ; through the points of division pass planes parallel to the plane of the bases ; the corresponding sections...
Page 220 - If a line is perpendicular to each of two lines at their point of intersection, it is perpendicular to their plane. Given FB perpendicular at B to each of two straight lines AB and BC of the plane MN. To prove FB perpendicular to the plane MN.
Page 254 - A truncated pyramid is the portion of a pyramid included between the base and a plane not parallel to the base.
Page xlii - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.
Page 319 - The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters.