Plane Geometry

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Century Company, 1916 - Geometry, Plane - 276 pages

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Page 74 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C ' with Proof STATEMENTS Apply A A'B'C ' to A ABC so that A'B
Page 189 - 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 72 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.
Page 107 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 133 - The sum of the angles of a triangle is equal to a straight angle.
Page 41 - If two sides of a triangle are unequal, the angles opposite these sides are unequal, with the greater angle opposite the greater side.
Page 166 - The locus of a point at a given distance from a given point is the circumference described from the point with the given distance as radius.
Page 241 - 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 173 - If four quantities are in proportion, they are in proportion by inversion ; that is, the second term is to the first as the fourth is to the third.
Page 82 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.

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