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ABCD adjacent algebraic altitude base bisect bisector called chord circumference circumscribed common Construct contained corresponding diagonals diagram for Prop diameter difference distance divide draw drawn equal equilateral triangle equivalent exercises exterior angle figure Find find a point Find the area formed four geometrical given circle given line given point given triangle greater hexagon hypotenuse included inscribed interior intersecting isosceles triangle length less limit line joining mean proportional measured median meet midpoints opposite sides parallel parallelogram passes perimeter perpendicular polygon PROBLEM produced Proof PROPOSITION prove prove Proof quadrilateral quantities radii radius ratio rectangle regular polygon respectively right angle right triangle School segments sides similar square straight line student tangent THEOREM third transform transversal trapezoid triangle are equal unequal vertex
Page 148 - 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 180 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'.
Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 31 - The median to the base of an isosceles triangle is perpendicular to the base.
Page 209 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Page 130 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 71 - The midpoints of two opposite sides of a quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex.
Page 26 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.
Page 190 - The areas of two similar triangles are to each other as the squares of any two homologous sides.
Page 56 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.