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ABCD acute adjacent altitude angle approaches base bisector bisects called centre chord circumference circumscribed coincide common construct describe diagonals diameter difference distance divide draw equal equidistant equilateral triangle equivalent external extremities fall feet figure Find Find the area formed four given circle given line given point greater half Hence hexagon hypotenuse inches included inscribed intersecting joining length less limit locus maximum mean measured meet middle point number of sides parallel parallelogram pass perimeter perpendicular plane PROBLEM Proof proportional PROPOSITION prove quantities radii radius ratio rectangle regular hexagon regular polygon respectively right angle right triangle secant segments sides similar square straight line tangent THEOREM trapezoid triangle triangle ABC vertex vertices
Page 94 - Any two sides of a triangle are together greater than the third side.
Page 66 - 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 191 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 169 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Page 166 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 66 - If one acute angle of a right triangle is double the other, the hypotenuse is double the shorter leg.
Page 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 139 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.