Wentworth & Hills's Exercise Manuals: Geometry, Τεύχος 3Ginn & Company, 1889 |
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Σελίδα ix
... . All right angles are equal . 15. Corollary II . The sum of the adjacent angles formed by producing one side of an angle from the vertex is equal to 180 ° . 16. Corollary III . The sum of all the consecutive SYLLABUS . ix.
... . All right angles are equal . 15. Corollary II . The sum of the adjacent angles formed by producing one side of an angle from the vertex is equal to 180 ° . 16. Corollary III . The sum of all the consecutive SYLLABUS . ix.
Σελίδα xi
... producing each side in succession , is equal to 360 ° . TRIANGLES . 36. Theorem . Two triangles are equal if they have a side and the two adjacent angles equal , each to each . 37. Corollary . Two right triangles are equal if they have ...
... producing each side in succession , is equal to 360 ° . TRIANGLES . 36. Theorem . Two triangles are equal if they have a side and the two adjacent angles equal , each to each . 37. Corollary . Two right triangles are equal if they have ...
Σελίδα xx
... produced into segments proportional to the other two sides . SIMILAR TRIANGLES . 145. Definitions . Similar triangles , homologous angles , vertices , sides , bases , and altitudes . 146. Theorem . Two triangles are similar if they are ...
... produced into segments proportional to the other two sides . SIMILAR TRIANGLES . 145. Definitions . Similar triangles , homologous angles , vertices , sides , bases , and altitudes . 146. Theorem . Two triangles are similar if they are ...
Σελίδα 2
... producing the sides of an equiangular pentagon until they meet , and then erasing the sides of the pentagon . 17. Find the sum of the angles of a polygon of 20 sides . 18. The sum of the angles of a polygon is 48 right an- gles ; find ...
... producing the sides of an equiangular pentagon until they meet , and then erasing the sides of the pentagon . 17. Find the sum of the angles of a polygon of 20 sides . 18. The sum of the angles of a polygon is 48 right an- gles ; find ...
Σελίδα 4
... producing the base ) two right triangles are formed ; what relation exists between these two triangles and the original triangle , ( i . ) when the altitude lies within the orig- inal triangle , ( ii . ) when it lies without ? 37. Can a ...
... producing the base ) two right triangles are formed ; what relation exists between these two triangles and the original triangle , ( i . ) when the altitude lies within the orig- inal triangle , ( ii . ) when it lies without ? 37. Can a ...
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.