Plane and Solid Geometry |
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Page 4
... corresponds angle O ; the designation tion of AO , OB , and hence is like the form ab . A line proceeding from the vertex , turning al from the first arm to the second , is said to tu angle being greater as the amount of turning is g If ...
... corresponds angle O ; the designation tion of AO , OB , and hence is like the form ab . A line proceeding from the vertex , turning al from the first arm to the second , is said to tu angle being greater as the amount of turning is g If ...
Page 23
... Corresponding points lie on corresponding lines . ( b ) To a line - segment between two points corresponds the line- segment between the corresponding points . ( a ) Corresponding lines pass through corresponding points . ( b ) To the ...
... Corresponding points lie on corresponding lines . ( b ) To a line - segment between two points corresponds the line- segment between the corresponding points . ( a ) Corresponding lines pass through corresponding points . ( b ) To the ...
Page 25
... corresponding to the capital letters designating the opposite ver- tices , as in the figures of ths . 3 and 4 . EXERCISES . 36. Draw figures illustrating the definitions given after th . 3 . 37. Could th . 3 have been given , with the ...
... corresponding to the capital letters designating the opposite ver- tices , as in the figures of ths . 3 and 4 . EXERCISES . 36. Draw figures illustrating the definitions given after th . 3 . 37. Could th . 3 have been given , with the ...
Page 26
... corresponding parts of the other , the quadrilaterals are congruent . ( Either divide into triangles , or apply superposition at once . ) 48. How many perpendiculars can be drawn to a given line from a point outside that line ? Show ...
... corresponding parts of the other , the quadrilaterals are congruent . ( Either divide into triangles , or apply superposition at once . ) 48. How many perpendiculars can be drawn to a given line from a point outside that line ? Show ...
Page 38
... corresponding angles ; also ba Theorem 15. If a transversal of two of alternate angles equal , then ( 1 ) anj its alternate angle , ( 2 ) any angle is responding angle , and ( 3 ) any two in exterior , angles on the same side of t ...
... corresponding angles ; also ba Theorem 15. If a transversal of two of alternate angles equal , then ( 1 ) anj its alternate angle , ( 2 ) any angle is responding angle , and ( 3 ) any two in exterior , angles on the same side of t ...
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Common terms and phrases
a₁ ABCD altitude angles equal b₁ b₂ bisect bisectors called central angle chord circle circumcenter circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder DEFINITIONS diagonals diameter dihedral angle divided draw drawn edges equal angles equal bases equidistant equilateral EXERCISES face angles figure of th frustum geometry given line given point greater Hence hypotenuse inscribed interior angles intersection isosceles lateral area line-segment lune mid-points oblique opposite sides orthocenter parallel lines parallelogram perigon perimeter perpendicular plane polar polyhedral angle polyhedron prism prismatic space Prismatoid produced Proof pyramid quadrilateral radii radius ratio rectangle rectangular parallelepiped regular regular polygon respectively rhombus right angle segments Similarly slant height sphere spherical polygon spherical surface spherical triangle square straight angle straight line Suppose symmetric tangent tetrahedron Theorem transverse section trihedral vertex vertices volume
Popular passages
Page 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Page 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...
Page 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...
Page 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 107 - XLI. 2. The perpendicular bisector of a chord passes through the center of the circle and bisects the subtended arcs.
Page 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.
Page 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.
Page 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.
Page 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.
Page 94 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.