New Plane Geometry

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D. C. Heath & Company, 1908 - Geometry, Plane - 174 pages
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Page 138 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 117 - If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar.
Page 136 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.
Page 126 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Page 44 - If two triangles have two sides of 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.
Page 58 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 140 - Two similar triangles are to each other as the squares of their homologous sides.
Page 13 - The sum of all the angles on the same side of a straight line at a given point is equal to two right angles.
Page 124 - If two chords intersect within a circle, the product of the segments of one chord is equal to the product of the segments of the other.
Page 35 - If two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced.

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