An Examination Manual in Plane Geometry |
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An Examination Manual in Plane Geometry George Albert Wentworth,George Anthony Hill No preview available - 2016 |
Common terms and phrases
ABCD analysis angle formed angle opposite angles are equal apothem auxiliary lines base bisects circle is equal circles touch circumference Construct a circle construct a square Construct a triangle Corollary decagon deductions diameter distance divide Draw equal angles equal arcs equal circles equal to half equally distant equilateral triangle exterior angle feet Find the area given angle given circle given point given straight line given triangle Hint homologous sides hypotenuse HYPOTHESIS inches included angle inscribed angle inscribed regular intersect isosceles trapezoid isosceles triangle joining the middle legs locus mean proportional meet middle points number of sides opposite sides parallelogram perimeter perpendicular Plane Geometry Problem Propositions quadrilateral radii ratio rectangle regular hexagon regular polygon rhombus right angle right bisector right triangle secant segment SHEFFIELD SCIENTIFIC SCHOOL similar polygons similar triangles subtended tangent Theorem third side touch a given triangle ABC triangle is equal vertex
Popular passages
Page 106 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 127 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 110 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Page 129 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 126 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the Jingle.
Page 92 - Find the angle subtended at the centre of a circle by an arc whose length is equal to the radius of the circle.
Page 123 - The product of two sides of a triangle is equal to the product of the altitude on the third side and the diameter of the circumscribed circle.
Page 118 - DE'F, and consequently symmetrical with DEF. PROPOSITION XIII.—THEOREM. 55. Two triangles on the same sphere are either equal or symmetrical, when a side and two adjacent angles of one are equal respectively to a side and two adjacent angles of the other.
Page 129 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Page 122 - If the radius of a circle be divided in extreme and mean ratio, the greater segment is equal to one side of a regular inscribed decagon.