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ABCD altitude assumed base become bisected bisectors called chord circle circumference circumscribed common congruent considered construct converse COROLLARIES corresponding Definitions describe determined diagonals diameter difference distance divided division draw drawn equal equal angles Exercises exterior angles extremes figure Find four geometry given given line given point greater half Hence hypotenuse inscribed interior intersecting isosceles joining length less limit locus magnitudes measure meet mid-points Note opposite sides parallel parallelogram passes pencil perigon perimeter perpendicular placed plane polygon Problem produced Proof prop proportional PROPOSITION prove quadrilateral radius ratio rectangle regular remainder represented Required respectively right angle segments sides similar Similarly solution square step straight line student Suppose surface taken tangent Theorem transversal triangle true vertex vertices XVII zero
Side 172 - A line parallel to one side of a triangle divides the other two sides proportionally.
Side 186 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 121 - The perpendicular bisector of a chord passes through the center of the circle and bisects the arcs subtended by the chord.
Side 202 - That is, the number which represents its square units of area is the product of the two numbers which represent its base and altitude. For in prop. II, if R' = 1, the square unit of area, then a' and 6' must each equal 1, the unit of length.
Side 162 - If the product of two numbers equals the product of two other numbers, either two may be made the means and the other two the extremes of a proportion.
Side 38 - If two triangles have two sides of the one respectively equal to two sides of the other, and the...
Side 131 - An angle in a segment is greater than, equal to, or less than, a right angle, according as the segment is less than, equal to, or greater than, a semicircle.