 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...that the hypotenuse of a right triangle is its longest side. 2. By use of Theorem XVIII, prove that the perpendicular is the shortest line that can be drawn from a point to a straight line. (Compare § 77.) 3. If the crank AB mentioned in Ex. 3, p. 59, is so arranged that AC > AB (see the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...base ^i of an isos. A are equal. But this is impossible. .-. b > c. QED ZB > ZC, by hyp. 131. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. (115.) NOTE. The method used in the above proof is known as the indirect method or reductio... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...The base A of an isos. A are equal. But this is impossible. .-. b > c. QED ^B > ZC, by hyp. 131. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. (115.) NOTE. The method used in the above proof is known as the indirect method or reductio... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 296 pages
...AD, making Zx = ZC. AADC is isosceles. Why? Then AD=DC. BD+DA>BA. BD+DOBA. .-.BOBA. 185. Theorem. A perpendicular is the shortest line that can be drawn from a point to a straight line. Given CD drawn perpendicular to the line AB from the point C, and CE any other line drawn from the... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...(2) their sum is greater than half the sum of the sides of the triangle. PROPOSITION XXV. THEOREM 87. The perpendicular is the shortest line that can be drawn from a point to a A straight line. Given : PR _L to AB ; PC not _L. To Prove : PR < PC. Proof : Extend PR to X, making... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...straight line through the center of the circle and perpendicular to the plane of the circle. 449. COR. 3. The perpendicular is the shortest line that can be drawn from a point to a plane. 450. The distance from a point to a plane is the perpendicular drawn from the point to the plane.... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...opposite these angles are unequal, and the greater side is opposite the greater angle. § 185. Theorem. A perpendicular is the shortest line that can be drawn from a point to a straight line. § 186. Theorem. If two straight lines are drawn from a point in a perpendicular to a given line, cutting... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...impossible. ... b > c. 3.ED REASONS ZB > ZC, by hyp. The base 4 of an isos. A are equal. 7, by hyp. 131. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. (115.) NOTE. The method used in the above proof is known as the indirect method or reductio... | |
 | Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...BD is J. to AB. (?) Hence BD and BC coincide. (?) .'. BC lies in MN. (?) Proposition 211 Theorem QED The perpendicular is the shortest line that can be drawn from a point to a plane. Hypothesis. AB is the -l . drawn from A to the plane MN, and AC is any other line drawn from... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...~7 may follow the hints for Case I, but / CX I referred to the adjacent figure. /M / 422. Corollary. The perpendicular is the shortest line that can be drawn from a point to a plane. Given (see figure for Case II above) the plane M, and PC the perpendicular to M from P. To prove... | |
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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
