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Elementary Geometry Plane and Solid: For Use in High Schools and Academies
Thomas F. Holgate
No preview available - 2015
Elementary Geometry, Plane and Solid; For Use in High Schools and Academies
Thomas F 1859-1945 Holgate
No preview available - 2015
ABCD adjacent altitude base bisects boundaries called centre chord circle circular circumscribed coincide common cone construct contains COROLLARY cylinder DEFINITION described diagonals diameter dihedral angle distance divided draw drawn edges element equidistant equilateral EXERCISES face angles faces figure Find fixed formed four given given line-segment given plane given point greater half Hence identically equal inscribed intersect joining lateral area length less lies limit lying magnitudes mean measure meeting mid-point number of sides opposite sides pairs parallel parallel planes parallelepiped parallelogram pass perimeter perpendicular placed plane polygon polyhedron prism projection Proof Prop proportional PROPOSITION pyramid radii radius ratio rectangle regular regular polygon required to prove respectively right angles segments Show sides similar Similarly sphere spherical square straight line subtended tangent theorem third triangle trihedral unit vertex vertices volume
Page 187 - 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 55 - 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 76 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 43 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.
Page 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.
Page 27 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 200 - The area of a triangle is equal to half the product of its base by its altitude.
Page 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.