Wentworth & Hills's Exercise Manuals: Geometry, Τεύχος 3Ginn & Company, 1889 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 46.
Σελίδα x
... respectively parallel are equal or supplementary : equal , if both are acute or both obtuse ; supplementary , if one is acute and the other obtuse . 28. Theorem . Two angles whose sides are respectively perpendicular are equal or ...
... respectively parallel are equal or supplementary : equal , if both are acute or both obtuse ; supplementary , if one is acute and the other obtuse . 28. Theorem . Two angles whose sides are respectively perpendicular are equal or ...
Σελίδα 8
... respectively to the opposite sides , form another trian- gle , the sides of which are bisected by the vertices of the first triangle . Compare the triangles as to magnitude . 32. The three altitudes of a triangle meet in one point . 33 ...
... respectively to the opposite sides , form another trian- gle , the sides of which are bisected by the vertices of the first triangle . Compare the triangles as to magnitude . 32. The three altitudes of a triangle meet in one point . 33 ...
Σελίδα 9
... respectively . DEFG is a parallelogram , and CO = 20E . Show in a similar way that BH must also pass through O. 44. The lines drawn through two opposite vertices of a parallelogram , to the middle points of the opposite sides , divide ...
... respectively . DEFG is a parallelogram , and CO = 20E . Show in a similar way that BH must also pass through O. 44. The lines drawn through two opposite vertices of a parallelogram , to the middle points of the opposite sides , divide ...
Σελίδα 13
... respectively , find the angle which the tangent through the vertex A makes with the side BC . Under what condition will this tangent be par- allel to BC ? 16. A circle and an angle are situated in the same plane . What is the measure of ...
... respectively , find the angle which the tangent through the vertex A makes with the side BC . Under what condition will this tangent be par- allel to BC ? 16. A circle and an angle are situated in the same plane . What is the measure of ...
Σελίδα 14
... respectively , find the radius of a third circle which shall touch both the given circles and contain the smaller . $ 4. THEOREMS . 1. The radius which bisects an angle at the centre bisects the corresponding chord , and is ...
... respectively , find the radius of a third circle which shall touch both the given circles and contain the smaller . $ 4. THEOREMS . 1. The radius which bisects an angle at the centre bisects the corresponding chord , and is ...
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.