Plane Geometry

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Page 121 - 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 301 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 255 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Page 151 - In the same circle, or in equal circles, if two chords are unequally distant from the center, they are unequal, and the chord at the less distance is the greater.
Page 131 - ... the third side of the first is greater than the third side of the second.
Page 105 - If a perpendicular is dropped from the vertex of the right angle of a right triangle to the hypotenuse, prove that the two triangles thus formed and the given triangle are mutually equiangular.
Page 119 - If three or more parallels intercept equal parts on one transversal, they intercept equal parts on every transversal. Given the parallels AB, CD, and EF intercepting equal parts on the transversal MN.
Page 165 - If two angles of a triangle are equal, the sides opposite are equal.
Page 130 - If two triangles have two sides of one equal respectively to two sides of the other...
Page 73 - Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.

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