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" The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and... "
Elements of Geometry and Trigonometry: With Applications in Mensuration - Page 30
by Charles Davies - 1886 - 324 pages
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The Ontario High School Geometry: Theoretical

Alexander H. McDougall - Geometry - 1910 - 316 pages
...Hence v AC is neither = nor <AB, .-. AC>AB. 57.— Exercises 1. The perpendicular is the shortest st. line that can be drawn from a given point to a given straight line. _ X 2. ABCD is a quadrilateral, of which AD is the longest side, and BC the shortest....
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Elements of Solid Geometry

William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...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 line, cutting off equal...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Modern - 1912 - 360 pages
...right triangle the hypotenuse is longer than either of the legs. 227. COROLLARY 2. Of all the lines that can be drawn from a given point to a given line, the perpendicular is the shortest. EXERCISES 1. The angles at the extremities of the greatest side...
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...carpenter's square or a draftsman's triangle (see p. 103). PROPOSITION XI. THEOREM 161. Of all lines that can be drawn from a given point to a given line, only one is perpendicular to the given line. Given the line AB, the point C without it, and CD perpendicular...
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Plane Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...ZC. AADC is isosceles. Why? Then AD = DC. Why? BD+DA>BA. Why? BD+DOBA. 111 .-.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...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...the sides opposite are unequal, and the greater side is opposite the greater angle. 227. Of all lines that can be drawn from a given point to a given line, the perpendicular is the shortest. 228. In any triangle the sum of two sides is greater than the third...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...right triangle the hypotenuse is longer than either of the legs. 227. COROLLARY 2. Of all the lines that can be drawn from a given point to a given line, the perpendicular is the shortest. EXERCISES 1. The angles at the extremities of the greatest side...
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Plane Geometry

Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...numerical illustrations of Ineq. Ax. 4. PLANE GEOMETRY. BOOK I PROPOSITION XXVII. THEOREM 136. The perpendicular is the shortest line that can be drawn from a given point to a given straight line. Q Given the point P and the line AB, PQJ-AB, and PR oblique to AB. To prove PQ < PR....
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Solid Geometry

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...
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Practical Geometry

Thomas Tate (Mathematical Master, Training College, Battersea.) - 1860 - 404 pages
...increase again; and as P moves further and further to the right, 0 P increases without limit. Since the perpendicular is the shortest line that can be drawn from a given point to a given straight line, it is called the distance of the point from the line. Remember that the distance of...
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