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ABC and DEF ABCD altitude angle formed Apply base bisector bisects called chord circle circumf circumference circumscribed coincide common cone Construct contains converse COROLLARY cylinder DEFINITION described diagonals diameter difference dihedral angles divided Draw drawn edges equally distant equiangular equilateral triangle equivalent EXERCISE exterior angles extremities faces figure Find four given given circle given line given point greater half homologous included inscribed interior length less limit line joining mean measure meet middle points opposite sides parallel parallelogram parallelopiped pass perimeter perpendicular placed plane polygon prism prolonged Proof proportional PROPOSITION Prove pyramid quadrilateral radii radius ratio rectangle regular inscribed Required respectively right angles segments Show sides similar sphere spherical square straight line Suggestion surface tangent THEOREM third trapezoid triangle triangle ABC unequal unit vertex vertices volume Whence
Σελίδα 167 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Σελίδα 187 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 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.
Σελίδα 180 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.