## Wentworth & Hills's Exercise Manuals: Geometry, Issue 3 |

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Wentworth & Hills's Exercise Manuals, Issue 3 George Albert Wentworth,George Anthony Hill No preview available - 2016 |

### Common terms and phrases

acute angle adjacent angles altitude Analysis apothem Auxiliary triangles base bisector bisects chord circumference circumscribed construct a circle construct a triangle cubic decagon denote diagonals diameter 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 angle given circle given length given line given point given square given triangle hypotenuse inches inscribed regular intersection isosceles trapezoid isosceles triangle legs line drawn line parallel median method of loci middle points parallelogram perimeter perpendicular plane problem produced quadrilateral radii radius rectangle regular hexagon regular polygon rhombus right angles right cone right cylinder right triangle secant segment slant height solution sphere spherical square feet straight line tangents drawn Theorem total surface trapezoid triangle ABC vertex vertices yards

### Popular passages

Page 75 - To find the locus of a point such that the sum of the squares of its distances from two given points A, B is constant.

Page xix - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 2 - A pyramid 15 ft. high has a base containing 169 sq. ft. At what distance from the vertex must a plane be passed parallel to the base so that the section may contain 100 sq.ft.?

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 58 - 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 77 - OP= 4 inches, r = 4 inches. 16. 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...

Page xix - AREAS. 175. Definitions. Equivalent figures, area of a figure, units of area, transformation of a figure. 176. Theorem. Two rectangles having equal bases are to each other as their altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles are to each other as the products of their bases and altitudes. 178. Theorem. Area of a rectangle = base X altitude. 179. Theorem. Area of a square = square of one side. 180. Theorem. Area of a parallelogram...

Page xiv - A straight line drawn parallel to the base of a triangle, bisecting one of the sides, bisects the other also ; and the part intercepted between the two sides is equal to half the base. 72. Theorem. The median of a trapezoid is' parallel to the bases and equal to half their sum. 73. Theorem. Equidistant parallels divide every secant into equal parts. BOOK II. THE CIRCLE. THE CIRCLE AND STRAIGHT LINES. 74. Definitions. Circumference, circle, radius, diameter, arc, chord, semi-circumference, segment,...

Page 29 - 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 xiv - An isosceles trapezoid is a trapezoid whose non-parallel sides are equal. A pair of angles including only one of the parallel sides is called a pair of base angles. Pairs of base angles The median of a trapezoid is parallel to the bases and equal to onehalf their sum.