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" If a straight line is parallel to a plane, the intersection of the plane with any plane passed through the given line is parallel to that line. "
Key to the Exercises in Wells's New Geometry - Page 86
by Webster Wells - 1909
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...and is therefore parallel to it. PROPOSITION VII. THEOREM. 443. If a straight line is parallel t.> a plane, the intersection of the plane with any plane drawn through the line is parallel to the line. Let AB be parallel to the plane MN, and let CD be the intersection of MN with any plane drawn through...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...planes JL to the same st. line AB. But this is impossible. .-. MN is || to PQ. 7 (506) QED 517. COR. 1. If a straight line is parallel to a plane, the intersection of the plane with any plane passed through the line is parallel to the line. Let the student show this. 518. COR. 2. If a straight...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...Then AB and MN cannot meet, and are parallel (§ 397). PROPOSITION X. THEOREM. 415. If a straii/lit line is parallel to a plane, the intersection of the...plane drawn through the line is parallel to the line. -V TB Let the line AB be parallel to the plane MN; and let CD be the intersection of MN with a plane...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...397). PROPOSITION X. THEOREM. • 415) If a straight line is parallel to a plane, the intersec• tion of the plane with any plane drawn through the line is parallel to the line. Let the line AB be parallel to the plane MN; and let CD, be the intersection of MN with a plane drawn...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...Parallel lines AB and CD intercepted between parallel planes are equal. PROPOSITION VII. THEOREM ,l»40. If a straight line is parallel to a plane, the intersection of the plane with a plane passed through thc line is parallel to the line. GIVEN — the line BA parallel to the plane...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...Parallel lines AB and CD intercepted between parallel planes are equal. PROPOSITION VII. THEOREM . If a straight line is parallel to a plane, the intersection of the plane with a plane passed through the line is parallel to the line. GIVEN— the line BA parallel to the plane...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...it cannot meet CD (§ 52). Then AB and MN cannot meet, and are II (§ 397). PROP. IX. THEOREM. 412. If a straight line is parallel to a plane, the intersection...plane drawn through the line is parallel to the line. Given line AB II to plane MN; and line CD the intersection of MN with any plane AD drawn through AB....
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 pages
...passing through O and II to each of the lines AB and CD. § 522 M D' IT PROPOSITION IX. THEOREM. 525. If a straight line is parallel to a plane, the intersection of the plane with any plane passed through the given line is parallel to that line. Let the line AB be parallel to the plane MN,...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 180 pages
...it cannot meet CD (§ 52). Then AB and MN cannot meet, and are II (§ 397). PROP. IX. THEOREM. 412. If a straight line is parallel to a plane, the intersection of the plane with any plane draivn through the line is parallel to the line. Given line AB II to plane MN; and line CD the intersection...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...passing through O and II to each of the lines AB and CD. § 522 D' N PROPOSITION IX. THEOREM. 525. If a straight line is parallel to a plane, the intersection of the plane with any plane passed through the given line is parallel to that line. Let the line AB be parallel to the plane MN,...
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