Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 23
... and the same straight line . 6. Show that the two straight lines which bisect the two pairs of vertical angles are perpendicular to each other . PROPOSITION IX . THEOREM . 61. At a point in PERPENDICULAR AND OBLIQUE LINES . 23 3333.
... and the same straight line . 6. Show that the two straight lines which bisect the two pairs of vertical angles are perpendicular to each other . PROPOSITION IX . THEOREM . 61. At a point in PERPENDICULAR AND OBLIQUE LINES . 23 3333.
Σελίδα 47
... bisect the ZACB . In the ACE and BCE , = AC BC , CE CE , = ZACE LBCE ; = ..AACE △ BCE , ( two are equal when two sides and the included respectively to two sides and the included ..ZA = ZB , ( being homologous & of equal △ ) . Hyp ...
... bisect the ZACB . In the ACE and BCE , = AC BC , CE CE , = ZACE LBCE ; = ..AACE △ BCE , ( two are equal when two sides and the included respectively to two sides and the included ..ZA = ZB , ( being homologous & of equal △ ) . Hyp ...
Σελίδα 48
... bisects the base . C B E Let the line CE bisect the ACB of the isosceles ДАСВ . We are to prove = I. A ACE △ BCE ; II . line CEL to AB ; III . A E = BE . I. In the ACE and BCE , = AC BC , = CE CE , ZACE Z BCE . = ..A ACE - ABCE , Hyp ...
... bisects the base . C B E Let the line CE bisect the ACB of the isosceles ДАСВ . We are to prove = I. A ACE △ BCE ; II . line CEL to AB ; III . A E = BE . I. In the ACE and BCE , = AC BC , = CE CE , ZACE Z BCE . = ..A ACE - ABCE , Hyp ...
Σελίδα 50
... bisect EBC . In the A E B F and CBF Draw E F. EB = BC , BF , BF LEBF - LCBF , .. the AEBF and CBF are equal , Hyp . Iden . Cons . § 106 ( having two sides and the included of one equal respectively to two sides Now and the included of ...
... bisect EBC . In the A E B F and CBF Draw E F. EB = BC , BF , BF LEBF - LCBF , .. the AEBF and CBF are equal , Hyp . Iden . Cons . § 106 ( having two sides and the included of one equal respectively to two sides Now and the included of ...
Σελίδα 54
... bisects the LB. Draw the Is OK , OP , and O H. In the rt . A O C K and OC P , OC = OC , = LOCK LOCP , = ..A OCK △ OCP , Iden . Cons . § 110 ( having the hypotenuse and an acute of the one equal respectively to the hypotenuse and an ...
... bisects the LB. Draw the Is OK , OP , and O H. In the rt . A O C K and OC P , OC = OC , = LOCK LOCP , = ..A OCK △ OCP , Iden . Cons . § 110 ( having the hypotenuse and an acute of the one equal respectively to the hypotenuse and an ...
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AABC ABCD altitude apothem arc A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide cone of revolution conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section S-ABC SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume