"Wentworth & Hill's Exercise Manuals: Geometry, Issue 3Ginn & Company, 1904 |
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Common terms and phrases
ABCD altitude Analysis apothem Auxiliary triangles base bisectors bisects centre chord circumference circumscribed construct a circle construct a triangle cubic decagon denote diagonals distance draw a line equidistant equilateral triangle equivalent find a point Find the area Find the length find the locus Find the radius Find the volume frustum given circle given length given line given point given square given triangle hypotenuse inches intersection isosceles trapezoid isosceles triangle join L₁ legs line drawn line parallel median method of loci middle points P₁ parallelogram perimeter perpendicular plane problem produced quadrilateral radii radius rectangle regular hexagon regular polygon rhombus right cone right cylinder right triangle secant segment similar slant height sphere square feet straight line tangent tangents drawn Theorem trapezoid triangle ABC vertex vertices yards
Popular passages
Page xxiii - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 81 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page xiv - 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 85 - To find the locus of points from which two given circles will be seen under equal angles. Show that the distances from any point in the locus to the centres of the two circles are as the radii of the circles; this reduces the problem to Ex. 12. 17. To find the locus of the points from which a given straight line is seen under a given angle. 18. To find the locus of the vertex of a triangle, having given the. base and the ratio of the other two sides. 19. To find the locus of the points in a plane...
Page 64 - In any triangle, the product of two sides is equal to the square of the bisector of the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab = t
Page 65 - The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the mid-points of the diagonals.
Page xxiii - Two parallelograms having equal altitudes are to each other as their bases. 2. Two parallelograms having equal bases are to each other as their altitudes.
Page 37 - A cone, whose slant height is equal to the diameter of its base, is inscribed in a given sphere, and a similar cone is circumscribed about the same sphere.
Page 8 - 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 6 - The sum of the perpendiculars dropped from a point in the base of an isosceles triangle to the legs is constant and equal to the altitude upon a leg.