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" 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... "
Solid Geometry - Page 222
by Walter Burton Ford, Charles Ammerman - 1913 - 107 pages
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 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...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...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...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 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...
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Cornell University Register and Catalogue

Cornell University - 1880 - 868 pages
...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,...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...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...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 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...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1891 - 344 pages
...then pass a plane through the point perpendicular to this line. PROPOSITION X.— THEOREM. 23. If tivo angles, not in the same plane, have their sides respectively parallel and lying in the same direction, they are e.Qual and their planes are parallel. Let BAG, B'A'C', be two...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...of points 11. Equidistant from two given planes, and two given points. PROPOSITION X. THEOREM. 47. 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. Notation. Let m, n (determining...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...plane, and then pass a plane through the point perpendicular to this line. PROPOSITION X.—THEOREM. 23. If two angles, not in the same plane, have their sides respectively parallel and lying in the same direction, they are eaual and their planes are parallel. Let BAC, B'A'C', be two...
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