If two angles not in the same plane have their sides respectively parallel and lying on the same side of the straight line joining their vertices, they are equal, and their planes are parallel. Let the corresponding sides of angles A and A' in the planes... The Teaching of Geometry - Page 299by David Eugene Smith - 1911 - 339 pagesFull view - About this book
| Elias Loomis - Conic sections - 1849 - 226 pages
...same plane, 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... | |
| William Chauvenet - Geometry - 1871 - 368 pages
...plane, the plane of these lines is parallel to the given plane. v, PROPOSITION XIII.— 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... | |
| William Chauvenet - Geometry - 1872 - 368 pages
...given plane, the plane of these lines is parallel to the given plane. PROPOSITION XIII— 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... | |
| 1876
...area of a trapezoid ? how, that of a regular polygon ? • II. — Solid and Spherical Geometry. 6. **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. 7. If a pyramid be cut by a plane... | |
| George Albert Wentworth - Geometry - 1877 - 402 pages
...are II if all the points of either be equally distant from the other). PROPOSITION X. THEOREM. 462. **If two angles not in the same plane have their sides respectively parallel and lying** in the same direction, they are equal. M Let AA and A' be respectively in the planes MN and PQ and... | |
| Elias Loomis - Geometry - 1877 - 443 pages
...same plane, they will be parallel to each other (Pr. 9), and consequently equal. G PROPOSITION XV. **THEOREM. If two angles not in the same plane have their sides** parallel to each other and similarly situated, these angles will be equal, and their planes will be... | |
| Wm. H. H. Phillips - 1878
...perpendicular to a 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 ||... | |
| Cornell University - 1880
...polyedrons, a spherical triangle, the ordinate of a point on a curve, the subtangent of a parabola. 2. **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. 3. Two triangular pyramids, having... | |
| W. E. BYERLY - 1887
...Through any given point one plane can be passed parallel to a given plane, and but one. PROPOSITION X. **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. PROPOSITION XI. If one of two... | |
| Edward Albert Bowser - Geometry - 1890 - 393 pages
...plane of these lines is parallel to the given plane. SOLID GEOMETRY. Proposition 1 1 . Theorem. 525. **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. Hyp. Let Zs A and A' lie in the... | |
| |