Exercises Contained in Wentworth's Geometry: With Key, Followed by a Selection of Miscellaneous Exercises for Practice

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Ginn & Heath, 1879 - 182 pages
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Page 16 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 8 - Every point in the bisector of an angle is equally distant from the sides of the angle...
Page 79 - If two triangles have two sides of the one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, then the included angle of the first is greater than the included angle of the second. [Converse of Prop. XXX.] BC B' C
Page 6 - ABC and ABD are two triangles on the same base AB, and on the same side of it, the vertex of each triangle being without the other. If AC equals AD, show that BC cannot equal BD (§ 154).
Page 160 - Find the locus of a point which moves so that the difference of the squares of its distances from two fixed points is constant.
Page 108 - The vertical angle of any oblique-angled triangle inscribed 'in a circle is greater or less than a right angle, by the angle contained by the base and the diameter drawn from the extremity of the base.
Page 123 - If from one of the equal angles of an isosceles triangle a perpendicular be drawn to the opposite side, the rectangle contained by that side and the segment of it intercepted between the perpendicular and base, is equal to the half of the square described upon the base.
Page 18 - ABC be formed by the intersection of three tangents to a circumference whose centre is 0, two of which, AM and AN, are fixed, while the third, BC, touches the circumference at a variable point P; show that the perimeter of the triangle ABC is constant, and equal to AM + AN, or 2 A M.
Page 120 - If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other side.
Page 90 - Prop. 2- The sum of the diagonals of a quadrilateral is less than the sum of any four lines that can be drawn from any point whatever (except the intersection of the diagonals) to the four angles.

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