Plane Geometry

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Page 248 - In order to prove two triangles similar : 1. Show that their angles are respectively equal. 2. Show that an angle of one is equal to an angle of the other, with the including sides proportional. 3. Show that their sides are respectively proportional. 4. Show that they are right triangles and have (a) a pair of acute angles equal, or (b) two pairs of corresponding sides proportional. 5. Show that they are isosceles triangles and have (a) their vertex angles, or
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 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 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 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 156 - Conversely, if .the. sum of two opposite sides of a quadrilateral is equal to the sum of the other two sides, then a circle may be inscribed in the quadrilateral.
Page 125 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.
Page 75 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Page 281 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.

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