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a₁ ABCD altitude angles equal b₁ b₂ bisect bisectors C₁ called central angles chord circle circumcenter circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder DEFINITIONS diagonals diameter dihedral angle divided draw drawn edges equal angles equidistant equilateral EXERCISES face angles figure of th frustum geometry given line given point greater Hence hypotenuse inscribed interior angles intersection isosceles triangle line-segment locus lune meet mid-points oblique opposite sides orthocenter P₁ P₂ parallel lines parallelepiped parallelogram perigon perimeter perpendicular plane plane geometry polar polyhedral angle prism Prismatoid produced Proof prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively rhombus right angle right-angled triangle segments Similarly slant height sphere spherical polygon spherical surface spherical triangle square straight angle straight line Suppose symmetric tangent tetrahedron Theorem trihedral vertex vertices
Σελίδα 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Σελίδα 24 - The third side is called the base of the isosceles triangle, and the equal sides are called the sides. A triangle which has no two sides equal is called a scalene triangle. The distance from one point to another is the length of the straight line-segment joining them. The distance from a point to a line is the length of the perpendicular from that point to that line. That this perpendicular is unique will be proved later. This is the meaning of the word distance in plane geometry. In speaking of...
Σελίδα 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...
Σελίδα 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Σελίδα 107 - XLI. 2. The perpendicular bisector of a chord passes through the center of the circle and bisects the subtended arcs.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.