 XVIII, prove that the perpendicular is the shortest line that can be drawn from a point to a straight line.  Plane Geometry - Page 74by Walter Burton Ford, Charles Ammermann - 1923 - 232 pagesFull view - About this book
 | 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...b > c. QED REASONS ZB > ZC, by hyp. The base A of an isos. A are equal. 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... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1923 - 414 pages
...growth of a side of a triangle means the growth of the angle opposite." RECTILINEAR FIGURES [I, §80 MISCELLANEOUS EXERCISES 1. Prove that the hypotenuse...that AC > AB (see the figure), show that the angle ACE will always remain less than half the angle XAB during the rotation. 4. If the pans of a balance... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...parallel, and angles gotten from our parallels, together, make the sum of the angles of the triangle. 145. The perpendicular is the shortest line that can be drawn from a point without to a given straight line. There are many ways of establishing this and kindred geometrical... | |
 | Great Britain. Parliament. House of Commons - Bills, Legislative - 1864 - 700 pages
...joining their point of intersection is bisected at right angles by the line joining their centres. 3. The perpendicular is the shortest line that can be drawn from a given point to a given straight line ; and of any two oblique lines, that which is nearer to the perpendicular... | |
| |
