 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
 | Daniel Alexander Murray - Spherical trigonometry - 1908 - 132 pages
...a line perpendicular to a radius at its extremity is tangent to the sphere. [Suggestion for proof : The perpendicular is the shortest line that can be drawn from a point to a plane.] A tangent to an arc of a great circle at any point of the arc is perpendicular to the radius... | |
 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...a line perpendicular to a radius at its extremity is tangent to the sphere. [Suggestion for proof : The perpendicular is the shortest line that can be drawn from a point to a plane.] A tangent to an arc of a great circle at any point of the arc is perpendicular to the radius... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...is the shortest straight line that can be drawn from a point to a straight line ; and, conversely, the shortest line that can be drawn from a point to a straight line is perpendicular to the line. Given : PC _L AB and any oblique p line PD. To Prove : PC < PD. Proof... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...£. Hence 2£ Cj&Z> is not a right angle. § 51 .-. CEisnot±AB. §52 PROPOSITION XV. THEOREM. 116. The perpendicular is the shortest line that can be drawn from a given point to a given line. Given the straight line AB, the point P, the _L PC, and any other line,... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...115. Only one perpendicular can be drawn from a given external point to a given straight line. 116. The perpendicular is the shortest line that can be drawn from a given point to a given line. 117. Two oblique lines from the same point in the perpendicular to a given... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...CD to a line AB (Fig. 48) unequal oblique lines are drawn to the base AB, the longer of the oblique lines is opposite the larger of the two base angles....§ 77.) 3. If the crank AB mentioned in Ex. 3, p. 59, is so arranged that AC > AB (see the figure, p. 59), show that the angle ACS will always remain... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...longer of the oblique lines is opposite the larger of the two base angles. ANGLES AND TRIANGLES 67 MISCELLANEOUS EXERCISES 1. Prove that the hypotenuse...§ 77.) 3. If the crank AB mentioned in Ex. 3, p. 59, is so arranged that AC > AB (see the figure, p. 59), show that the angle ACS will always remain... | |
 | 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... | |
| |
