Elementary Geometry, Plane and Solid: For Use in High Schools and AcademiesMacmillan, 1901 - 440 sider |
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Resultat 6-10 av 28
Side 90
... ABCD , if AB is the greatest side and CD the least , show that BCD is greater than DAB , and ≤ CDA greater than ZABC . 2. Show that the sum of the diagonals of a convex quadrilateral is greater than the sum of either pair of opposite ...
... ABCD , if AB is the greatest side and CD the least , show that BCD is greater than DAB , and ≤ CDA greater than ZABC . 2. Show that the sum of the diagonals of a convex quadrilateral is greater than the sum of either pair of opposite ...
Side 114
... ABCD be any convex quadrilateral inscribed in a given circle . It is required to prove that the angles BAD and BCD , also that the angles ABC and ADC are supplementary . Proof . Join AC and BD . Z BAC = △ BDC ; also ≤ DAC = ≤ DBC ...
... ABCD be any convex quadrilateral inscribed in a given circle . It is required to prove that the angles BAD and BCD , also that the angles ABC and ADC are supplementary . Proof . Join AC and BD . Z BAC = △ BDC ; also ≤ DAC = ≤ DBC ...
Side 115
... ABCD , ♧ ABC and ADC are supplementary . ZADC equals half of ZAOC , O being the centre of the circle . ( Prop . IX . ) ZABC equals half of the reflex angle 4 AOC . D The sum of ABC and ADC equals half of the sum of the two angles at 0 ...
... ABCD , ♧ ABC and ADC are supplementary . ZADC equals half of ZAOC , O being the centre of the circle . ( Prop . IX . ) ZABC equals half of the reflex angle 4 AOC . D The sum of ABC and ADC equals half of the sum of the two angles at 0 ...
Side 120
... ABCD inscribed in a circle are produced to meet in E , the triangles AEC and DEB are equiangular , as are also the triangles AED and CEB . 10. Divide a circle into two arcs such that the angle contained by one shall be twice the angle ...
... ABCD inscribed in a circle are produced to meet in E , the triangles AEC and DEB are equiangular , as are also the triangles AED and CEB . 10. Divide a circle into two arcs such that the angle contained by one shall be twice the angle ...
Side 135
... ABCD , and circles are described about DEA and BEC , show that the other point of intersection of these two circles must lie on BD . 25. If through P , any point on one of two circles which intersect at A and B , the straight lines PA ...
... ABCD , and circles are described about DEA and BEC , show that the other point of intersection of these two circles must lie on BD . 25. If through P , any point on one of two circles which intersect at A and B , the straight lines PA ...
Andre utgaver - Vis alle
Elementary Geometry, Plane and Solid: For Use in High Schools and Academies Thomas Franklin Holgate Uten tilgangsbegrensning - 1901 |
Elementary Geometry, Plane and Solid; for Use in High Schools and Academies Thomas F 1859-1945 Holgate Ingen forhåndsvisning tilgjengelig - 2018 |
Elementary Geometry Plane and Solid: For Use in High Schools and Academies Thomas F. Holgate Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
ABCD AC² adjacent angles altitude angle formed angles are equal apothem base bisector bisects centre chord coincide convex convex polygon COROLLARY DEFINITION diagonals diameter dicular dihedral angle draw equal angles equal in area equiangular equidistant equilateral triangle EXERCISES face angles figure given circle given line-segment given plane given point given straight line greater Hence hypotenuse identically equal interior angles isosceles triangle length Let ABC line perpendicular magnitudes measure mid-point number of sides opposite sides pair parallel planes parallelepiped parallelogram perimeter perpen plane angles point of contact point of intersection polyhedral angle polyhedron prism Proof Prop Proposition VIII pyramid quadrilateral radii radius ratio rectangle regular polygon required to prove respectively right angles right triangle segments side BC similar sphere square subtended supplementary angle surface tangent tetrahedron theorem triangle ABC triangle is equal trihedral vertex volume
Populære avsnitt
Side 187 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 230 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Side 55 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Side 76 - 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.
Side 43 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.
Side 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.
Side 27 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Side 200 - The area of a triangle is equal to half the product of its base by its altitude.
Side 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Side 229 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.