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ABCD altitude analysis angle formed angle opposite angles are equal apothem auxiliary lines base 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 equidistant equilateral triangle exterior angle feet Find the area Find the locus 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 middle points number of sides opposite sides parallelogram perimeter perpendicular Plane Geometry Propositions quadrilateral ratio rectangle regular hexagon regular polygon rhombus right angle right bisector right triangle secant segment SHEFFIELD SCIENTIFIC SCHOOL similar triangles subtended tangent Theorem third side touch a given triangle ABC triangle is equal vertex
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 120 - ... 4. Show that the areas of similar triangles are to each other as the squares of the homologous sides.
Page 104 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
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 138 - A line which divides two sides of a triangle proportionally is parallel to the third side.
Page 116 - ... 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.