Modern Methods in Elementary GeometryMacmillan, 1868 - 112 σελίδες |
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Σελίδα 8
... PARALLELS . A BE D FGC Parallel straight lines are such as being produced ever so far both ways do not meet . If a straight line EF cut the two straight lines AB , CD , it makes with either of them four angles which we will denote by ...
... PARALLELS . A BE D FGC Parallel straight lines are such as being produced ever so far both ways do not meet . If a straight line EF cut the two straight lines AB , CD , it makes with either of them four angles which we will denote by ...
Σελίδα 9
... parallel to CD . COR . 2. If the alternate angle AGH is equal to the alternate angle GHD , AB is parallel to CD . For AGH EGB . - COR . 3. If the two interior angles BGH , THE STRAIGHT LINE , 9.
... parallel to CD . COR . 2. If the alternate angle AGH is equal to the alternate angle GHD , AB is parallel to CD . For AGH EGB . - COR . 3. If the two interior angles BGH , THE STRAIGHT LINE , 9.
Σελίδα 10
... parallel to CD . For BGH + GHD will then be equal to BGH + EGB , and therefore EGB = GHD . THEOREM VIII . If AB be parallel to CD , then shall the angle EGB be Ꮮ A- -B M H C- equal to the angle GHD . For if not let EGM be equal to GHD ...
... parallel to CD . For BGH + GHD will then be equal to BGH + EGB , and therefore EGB = GHD . THEOREM VIII . If AB be parallel to CD , then shall the angle EGB be Ꮮ A- -B M H C- equal to the angle GHD . For if not let EGM be equal to GHD ...
Σελίδα 11
... parallel to one another . E Draw EFHG cutting AB , KL , and CD , in F , H , and G. F A B H Then EFB = FHL . K Ꮮ G And = FHL HGD . C D Therefore EFB = HGD . Therefore AB is parallel to CD . I. 7 . TRIANGLES . THEOREM X. If one side BC ...
... parallel to one another . E Draw EFHG cutting AB , KL , and CD , in F , H , and G. F A B H Then EFB = FHL . K Ꮮ G And = FHL HGD . C D Therefore EFB = HGD . Therefore AB is parallel to CD . I. 7 . TRIANGLES . THEOREM X. If one side BC ...
Σελίδα 19
... parallel . THEOREM XVI . The opposite sides and angles of parallelograms are equal . Let ABCD be a parallelogram . Then shall AB = CD , BC = DA , A B AC , and B = D. Join BD . D Then the alternate angle ABD = the alternate angle CDB ...
... parallel . THEOREM XVI . The opposite sides and angles of parallelograms are equal . Let ABCD be a parallelogram . Then shall AB = CD , BC = DA , A B AC , and B = D. Join BD . D Then the alternate angle ABD = the alternate angle CDB ...
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A'BC Algebra alternate angle altitude angle equal arc CD ARITHMETIC bisect BROOKE FOSS WESTCOTT Cambridge centre circle touching circumference cloth coincide congruent CONIC SECTIONS contain convex angle convex polygon Crown 8vo diagonals diameter dicular divide duplicate ratio Edward Thring ELEMENTARY TREATISE equal angles equally distant equally remote equiangular equiangular and similar equilateral triangle Examples exterior angle Fcap Find the locus GEOMETRY given angle given circle given line given point given straight line greater Hence intersect isosceles John's College late Fellow Let ABCD line drawn MATHEMATICAL measure meet middle point opposite sides parallel to BC parallelogram perpen perpendicular polygon produced quadrilateral figure radius rectangle right angles right-angled triangle Schools Second Edition segments Shew shortest line similar triangles student subtend tangent THEOREM THEOREM VII Third Edition trapezium triangle ABC vertex