...planes are equal, and therefore parallel planes are equidistant. PROPOSITION XXI. (44) If two angles have their sides respectively parallel and lying in the same direction, they will be equal, and their planes will be parallel. If they be in the same plane, the proposition has...

...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...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...

...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...direction, they are equal and their planes are parallel. Let BA C,B'A' C', be two angles lying in the planes MN, M'N'; and let AB, AC, be parallel respectively...

...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...direction, they are equal and their planes are parallel. 7. If a pyramid be cut by a plane parallel to its base : 1st, the edges and the altitude will be divided...

...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...parallel and lying in the same direction, they are equal. M Let AA and A' be respectively in the planes MN and PQ and have AD parallel to A' D' and AC parallel...

...of either be equally distant from the other). GEOMETIiY. — BOOK VI. PROPOSITION X. THEOREM. 462. If two angles not in the same plane have their sides...parallel and lying in the same direction, they are ctfital. M Let AA and A' be respectively in the planes MN ana PQ and have AD parallel to A' D' and...

...ofeither be equally distant from the other). QED 262 GEOMETRY. — BOOK VI. PROPOSITION X. THEOREM. 462. If two angles not in the same plane have their sides...respectively parallel and lying in the same direction, thetj are equal. M Let AA and A' be respectively in the planes MN and PQ and have AD parallel to A'...

...D A L GEOMETRY. BOOK VI. PROPOSITION X. THEOREM. 462. If two angles not in the same plane have then 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 have AD parallel to A' D' and AC parallel...

...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...parallel and lying in the same direction, they are eaual and their planes are parallel. Let BAG, B'A'C', be two angles lying in the planes MN, M'N'; and...

...plane can be passed parallel to a given plane, and but one. PROPOSITION X. If two angles,, not in tlie same plane, have their sides respectively parallel...direction, they are equal and their planes are parallel. PROPOSITION XI. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular...