 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...between two given straight lines. 61. Bisect a triangle by a line drawn parallel to one of its sides. 62. The sum of the perpendiculars drawn from any point within an equilateral triangle to the sides, is equal to the perpendicular from either angle to its opposite side. 63. If from the extremities... | |
 | Euclides - 1860 - 288 pages
...sum will be equal to the perpendicular from either extremity of the base upon the opposite side. 27. The sum of the perpendiculars drawn from any point within an equilateral triangle on the sides, is equal to the perpendicular from any of the angular points upon the opposite side.... | |
 | Adrien Marie Legendre - Geometry - 1882 - 194 pages
...of the scale taken and construct on it a square, as before. fi. — Show that the sum of the. three perpendiculars, drawn from any point within an equilateral triangle to the three sides, is equal U the altitude of the triangle. Let ABC be an equilateral triangle, and BD its altitude. From O, a... | |
 | Euclides - 1884 - 434 pages
...prove that CO produced will divide AB into two segments in the ratio of 9 to 1. 10. Perpendiculars are drawn from any point within an equilateral triangle to the three sides. Prove that their sum is constant. 11. Triangles and [r8 are to one another in the ratio compounded... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...whose sides are respectively 16, 12, 8, 4, and 2 units in length. 5. Show that the sum of the three perpendiculars drawn from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. 6. Show that the sum of the squares of two lines, drawn from any point in... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...The rectangle contained by two sects is a mean proportional between their squares. 100. The sum of perpendiculars drawn from any point within an equilateral triangle to the three sides equals its altitude. 101. The bisector of an angle of a triangle divides the triangle into two others,... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...The rectangle contained by two sects is a mean proportional between their squares. 100. The sum of perpendiculars drawn from any point within an equilateral triangle to the three sides equals its altitude, 101. The bisector of an angle of a triangle divides the triangle into two others,... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...AC. Draw P& J. to BF, and prove the A PBG and PBD equal. p 74. The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude. HINT. Draw through the point a line II to the base, and apply... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...from any point in the base is constant (see Ex. 133). Show also that the sum of the perpendiculars from any point within an equilateral triangle to the three sides is constant. Ex. 681.— ABC, DBC are two triangles on the same base BC : the line joining the vertices... | |
 | James Andrew Blaikie, William Thomson - Geometry - 1891 - 154 pages
...Draw PL || A B. Use Euc. I. 29, I. 5, and I. 26 to show that CL=PR; and deduce that PQ± PR = CD. 14. The sum of the perpendiculars drawn from any point within an equilateral triangle to its sides is constant. Let PQ, PR, PS be the perpendiculars. Draw LPM || BC ; AD and MN || PS; MO ||... | |
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The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig. 
