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ABCD acute altitude axis base bisector bisects called chord circle circumscribed coincides common congruent construct converse COROLLARY corresponding definition describe diagonal diameter difference distance divide Draw drawn equal equal sides equilateral EXERCISES exterior angle feet figure Find geometry given given circle given point greater half hypotenuse Imagine inch included inscribed intersecting isosceles triangle length less letters line segment mean measure median meet method mid-point miles Note observed opposite opposite sides parallel parallel lines parallelogram passes perpendicular places plane polygon position PROBLEM produced Proof proportional prove quadrilateral radius ratio rectangle regular polygon represent respectively right angle right triangle rotate Show sides similar solution square straight line student subtended SUGGESTION supplementary Suppose symmetric with respect symmetry tangent THEOREM third transversal trapezoid triangle turned vertex vertices
Side 201 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Side 61 - 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 182 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Side 78 - ... the angle opposite the third side of the first triangle is greater than the angle opposite the third side of the second.
Side 160 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Side 166 - 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'.
Side 177 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.