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ABCD acute altitude angle approaches base bisectors bisects called chord circle circumference circumscribed coincide common Compute CONCLUSION cone constant construct COROLLARY cylinder DEFINITIONS describe diagonals diameter diedral angles difference distance divided Draw drawn edges equal equidistant equilateral triangle equivalent faces feet figure Find formed four given given line given point greater half homologous hypotenuse HYPOTHESIS inches included inscribed intersect isosceles triangle joining legs less limit measured median meet opposite parallel parallelogram passes perimeter perpendicular plane polyedron polygon prism PROBLEM produced PROOF proportional PROPOSITION Prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively right angles right triangle segments sides similar SOLUTION sphere square straight line surface symmetrical tangent THEOREM third trapezoid triangle triangle ABC vertex vertices volume
Page 168 - 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 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 35 - Any side of a triangle is less than the sum of the other two sides...
Page 242 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Page 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 192 - The areas of two rectangles having equal altitudes are to each other as their bases.