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acute angle adjacent angles adjacent sides altitude angle ABC angles formed base bisects called central angles chord circle with center circumscribed coincides construct a triangle convex polygon COROLLARY corresponding cosine describe a circle diagonal diameter distance divide Draw equal angles equal sides equiangular polygon equilateral triangle EXERCISES exterior angle exterior tangents feet Find the area FUNDAMENTAL PROPOSITION geometry given circle given line segment given point given straight line given triangle hypotenuse inches included angle inscribed intersecting isosceles trapezoid isosceles triangle Let the student mid-point number of sides opposite sides parallel lines parallelogram perimeter plane PROBLEM quadrilateral radian radii radius ratio rectangle regular polygon rhombus right angle right triangle rotate segment joining subtended symmetric with respect tangent THEOREM third side transversal trapezoid triangle ABC triangle are equal vertex vertices
Page 203 - 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.
Page 63 - 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.
Page 184 - 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.
Page 80 - ... the angle opposite the third side of the first triangle is greater than the angle opposite the third side of the second.
Page 162 - 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.
Page 168 - 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 179 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.