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ABC and DEF ABCD altitude Apply base bisector bisects called chord circle circumference circumscribed coincide common cone Construct contains CONVERSELY COROLLARY cutting cylinder DEFINITION described diagonals diameter difference dihedral angles divided Draw drawn edges equally distant equilateral triangle equivalent EXERCISE exterior angles extremities faces figure Find four frustum given given line given point greater half homologous included increased inscribed isosceles lateral area length less Let ABC limit line joining mean measure meet middle points parallel parallelogram parallelopiped pass perimeter perpendicular plane polygon polyhedron prism prolonged Proof proportional PROPOSITION Prove pyramid quadrilateral radii radius ratio rectangle Required respectively right angles segments Show sides similar sphere spherical square straight line surface tangent tetrahedron THEOREM third trapezoid triangle triangle ABC unequal unit vertex vertices volume Whence
Page 167 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 187 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 202 - In any triangle, the square of the 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 upon that side.
Page 180 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Page 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Page 195 - Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig.
Page 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.