 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" in planes MN and PQ, respectively, with AB and AC II respectively to A'B' and AC',...  Key to the Exercises in Wells's New Geometry - Page 87by Webster Wells - 1909Full view - About this book
 | Elias Loomis - Conic sections - 1849 - 252 pages
...they will be parallel to each other (Prop. IX.), and, consequently, equal. PROPOSITION XV. THEOREM. If two angles, not in the same plane, have their sides parallel and similarly situated, these angles will be equal, and their planes will be parallel. Let the two angles... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...parallel to each other (Prop. X. Cor. 1) ; and consequently equal. PROPOSITION XVI. — THEOREM. 424. 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 BAC,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...parallel to each other (Prop. X. Cor. 1) ; and consequently equal. PROPOSITION XVI. — THEOREM. 424. 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 BAC,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...parallel to each other (Prop. X. Cor. 1) ; and consequently equal. PROPOSITION XVI. — THEOREM. 424. 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 BAC,... | |
 | Francis Henney Smith - Geometry, Descriptive - 1868 - 86 pages
...lines, comprised between two parallel planes, are equal. (El. Geo., Book V. Prop. XVI.) PROP. XXIII. If two angles, not in the same plane, have their sides parallel and lying in the same direction, they will be equal, and the planes of the angles will be parallel. (El.... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...plane MN passing through its foot, is perpendicular to the plane MN. Therefore, etc. THEOREM VIII. If two angles not in the same plane have their sides parallel and lying in the same direction, the angles will be equal and their planes parallel. Let SAC and.DEF'be... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...parallel to each other (Prop. X. Cor. 1) ; and consequently equal. PROPOSITION XVI. — THEOREM. 424. 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 BAC,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...THEOREM. 32. If two angles, not in the same plane, have their sides respectively/ parallel and lying in the same direction, they are equal and their planes are parallel. Let BA C, B'A'C', be two angles lying in the af planes MN, M'N'; and let AB, AC, be parallel respectively... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...the quadrilateral AD being parallel^ the figure is a parallelogram ; therefore AC=BD. THEOREM IV. 11. 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 ^... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...sides of the quadrilateral AD being parallel, the figure is a parallelogram ; therefore THEOREM .IV. H, 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 D EF be two angles... | |
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