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ABCD altitude angle approaches base bisector bisects called chord circle circumscribed coincide common congruent construct COROLLARY corresponding cube cylinder describe diagonal diameter difference dihedral angles distance divide draw drawn equal equidistant equivalent EXERCISE faces figure Find follows formed four frustum geometry given line given point greater half Hence included inscribed intersection isosceles joining lateral area length less limit locus measured meet mid-point opposite parallel parallel lines parallelogram pass perimeter perpendicular placed plane plane MN polygon polyhedron prism PROBLEM Proof proportional PROPOSITION prove pyramid radii radius ratio rectangle rectangular parallelepiped regular regular polygon regular pyramid relation respectively right angle segments shown sides similar slant height solid sphere square straight line Suppose surface symmetric tangent THEOREM third triangle triangle ABC triangular vertex vertices volume
Side 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Side 188 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Side 150 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Side 54 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Side 31 - In an isosceles triangle the angles opposite the equal sides are equal.
Side 77 - 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...
Side 51 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 22 - The following are the most important axioms used in geometry: 1. If equals are added to equals the sums are equal. 2. If equals are subtracted from equals the remainders are equal. 3. If equals are multiplied by equals the products are equal. 4. If equals are divided by equals the quotients are equal.