 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...plane that is drawn perpendicular to the third Hue. BOOK V.] STRAIGHT LINES AND PLANES. v. Theorem. If two angles not in the same plane have their sides parallel each to each, and lying in the same direction, they are equal. HYPOTII. AB || DE, and AC || DF. To... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...quadrilateral AD being parallel, the figure is a parallelogram; therefore AC = B D. THEOREM X. 28. If two angles not in the same plane have their sides parallel and similarly situated, the angles are equal and their planes parallel. Let ABC and DEF be two angles in... | |
 | Charles Scott Venable - 1881 - 380 pages
...Cor. 1) ; hence they are equal. 194 PROPOSITION XVIII. THEOREM. If two angles, CAE, DBF, not situated in the same plane, have their sides parallel and lying...same direction, these angles will be equal, and their plams will be parallel. Take AC = BD, AE = BF, and join CE, DF, AB, CD, EF. Since AC is equal and parallel... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...it will be perpendicular to A and B (Cor. I); .-. A and B, by theorem, are parallel. M THEOREM VIII. If two angles, not in the same plane, have their sides parallel and in the same direction, the angles 'will be equal and their planes parallel. Let the angles A and B... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...planes are every-where equally distant. BOOK VI. PROPOSITION XIII. THEOREM. If two angles, not situated in the same plane, have their sides parallel, and lying in the same direction, the angles are equal and their planes parallel. Let CAE and DBF be two angles lying in the planes MN... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...parallel to AB and AC. Then DE and DF lie in the plane PQ (§ 444). PROPOSITION XII. THEOREM. 455. If two angles not in the same plane have their sides parallel and extending in the same direction, they are equal and their planes are parallel. Let JOT~ and PQ be the... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...XVI. The intersections of two parallel planes with a third plane are parallel lines. PROPOSITION XVII. If two angles not in the same plane have their sides parallel and lying in the same direction from their vertices, they are equal and their planes are parallel. PROPOSITION XVIII. A .•.! i ..i;,i... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...Therefore but one plane can be drawn through A parallel to MN. QED PROPOSITION XVII. THEOREM. 398. // two angles not in the same plane have their sides parallel and extending in the same direction, they are equal, and their planes are parallel. Given — PQ and MN... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...MX at E. If line BE is perpendicular to CD, prove AE perpendicular to CD. PROP. XVII. THEOREM. 426. If two angles not in the same plane have their sides parallel and extending in the same direction, they are equal, and their planes are parallel. Given ABAC and B'A'C"... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...is perpendicular to CD, prove AE perpendicular to CD. (Fig. of Prop. VII.) PROP. XVII. THEOREM. 426. If two angles not in the same plane have their sides parallel and extending in the same direction, they are equal, and their planes are parallel. Given ^ BAC and B'A'C'... | |
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If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let... 
