Wentworth & Hills's Exercise Manuals: Geometry, Τεύχος 3Ginn & Company, 1889 |
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Σελίδα xii
... greater which is opposite the greater side . 48. Theorem . Of two sides of a triangle that is the greater which is opposite the greater angle . 149 , Theorem . If two triangles have two sides equal , each to each , but the included ...
... greater which is opposite the greater side . 48. Theorem . Of two sides of a triangle that is the greater which is opposite the greater angle . 149 , Theorem . If two triangles have two sides equal , each to each , but the included ...
Σελίδα xiii
... greater than their difference . 62. Theorem . The sum of two straight lines , drawn from a point to the ends of a straight line , is greater than the sum of any other two straight lines similarly drawn but included by them . 63. Theorem ...
... greater than their difference . 62. Theorem . The sum of two straight lines , drawn from a point to the ends of a straight line , is greater than the sum of any other two straight lines similarly drawn but included by them . 63. Theorem ...
Σελίδα xv
... greater than any other chord . 78. Theorem . Circles having equal radii or equal diam- eters are equal ; and conversely . 79. Theorem . In the same circle , or in equal circles , equal arcs are subtended by equal chords ; and conversely ...
... greater than any other chord . 78. Theorem . Circles having equal radii or equal diam- eters are equal ; and conversely . 79. Theorem . In the same circle , or in equal circles , equal arcs are subtended by equal chords ; and conversely ...
Σελίδα xvii
... greater than a semicircle is acute , and every angle inscribed in a segment less than a semicircle is obtuse . 103. Theorem . The angle formed by a tangent and a chord is measured by half the intercepted arc . 104. Theorem . An angle ...
... greater than a semicircle is acute , and every angle inscribed in a segment less than a semicircle is obtuse . 103. Theorem . The angle formed by a tangent and a chord is measured by half the intercepted arc . 104. Theorem . An angle ...
Σελίδα 1
... greater than the one preced- ing it in order . Find all the angles . 8. Through the vertex of a right angle a line is drawn outside the angle . What is the sum of the two acute an- gles thereby formed ? 9. One acute angle of a right ...
... greater than the one preced- ing it in order . Find all the angles . 8. Through the vertex of a right angle a line is drawn outside the angle . What is the sum of the two acute an- gles thereby formed ? 9. One acute angle of a right ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude Analysis apothem Auxiliary triangles base bisectors 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 circle given length given line given point given square given triangle hypotenuse inches inscribed regular intersection isosceles trapezoid isosceles triangle join K₁ L₁ legs line drawn line parallel median method of loci middle points P₁ parallelogram perimeter perpendicular plane problem produced quadrilateral radii 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
Δημοφιλή αποσπάσματα
Σελίδα 79 - 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.
Σελίδα xxiii - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 6 - 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.?
Σελίδα 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.
Σελίδα 62 - 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
Σελίδα 81 - 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...
Σελίδα xxiii - 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...
Σελίδα 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,...
Σελίδα 33 - 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.
Σελίδα 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.