...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...

...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...

...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...

...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...

...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...

...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...

...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 ||...

...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...

...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...

...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...