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altitude approaches base bisected bisector called central angle chord circle circumference circumscribed common cone construct contains converse cylinder denote diagonals diameter difference dihedrals distance divided Draw drawn edges equal equilateral equivalent EXERCISES externally extremities faces figure Find fixed four Geometry given circle given line given point greater homologous inches included increased indefinitely inscribed intercepted intersect isosceles triangle lateral length less limit line joining locus lune magnitudes measure median normal NOTE number of sides opposite parallel parallelogram passes perimeter perpendicular plane polyhedron position prism PROBLEM proportional PROPOSITION Prove pyramid radii radius ratio rectangle regular polygon respectively right angles right triangle segments Show sides similar solid sphere spherical square straight line surface tangent tetrahedron THEOREM third trapezoid triangle triangle ABC trihedral unit variable vertex vertices volume
Σελίδα 33 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Σελίδα 152 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 13 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Σελίδα 197 - A sphere is a solid bounded by a surface, all the points of which are equally distant from a point within called the center.
Σελίδα 154 - Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.
Σελίδα 84 - If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third. Let...
Σελίδα 14 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Σελίδα 147 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Σελίδα 94 - ... 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.