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ABCD acute adjacent altitude angle approaches base bisector bisects called chord circle circumscribed coincide common congruent Cons Construct corresponding cutting describe diagonals diameter difference divided Draw drawn equal equidistant equivalent exterior extremities figure Find formed geometry given given circle given line given point Given the line greater half Hence hypotenuse included inscribed intercepted interior angles intersecting joining legs length less limit mean measured median meet mid-point parallel parallelogram passes perimeter perpendicular polygon PROBLEM Proof proportional PROPOSITION prove prove Given quadrilateral quantities radii radius ratio rectangle regular inscribed regular polygon respectively right angle right triangle secant segments sides similar Similarly square straight angle straight line tangent THEOREM trapezoid triangle variable vertex vertices Нур
Page 41 - 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 243 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Page 179 - 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 62 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 5 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.
Page 135 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Page 67 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.
Page 176 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.