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ABCD adjacent altitude analysis angle base bisector bisects centre chord circle is equal circumference circumscribed COLLEGE common conclusion Construct Construct a triangle contained Corollary deductions Define described diagonals diameter difference distance divide Draw drawn ends equal equal angles equal circles equilateral triangle equivalent EXAMPLE exterior feet figure Find Find the area Geometry given circle given point given straight line greater hexagon hypotenuse HYPOTHESIS inches included inscribed intersect isosceles triangle joining June known legs length line joining locus mean proportional measured meet method middle points opposite sides pair parallel parallelogram pass perimeter perpendicular Plane Problem proof Propositions Prove quadrilateral radius ratio rectangle regular hexagon regular polygon respectively right angle right triangle secant segment Show similar solving square tangent Theorem third side touch a given trapezoid triangle ABC triangle is equal unequal vertex vertices
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.