 | Adrien Marie Legendre - 1882 - 194 σελίδες
...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... | |
 | Charles Davies, Adrien Marie Legendre - 1885 - 538 σελίδες
...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... | |
 | George Albert Wentworth - 1888 - 264 σελίδες
...the two Js, BF the altitude upon AC. Draw PG ± to BF, and prove the A PSG and PBD equal. . . P 74. The sum of the perpendiculars dropped from any point...three sides is constant, and equal to the altitude. HINT. Draw through the point a line II to the base, and apply Ex. 73. 75. What is the locus of all... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...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 A and D... | |
 | Euclid - 1892 - 460 σελίδες
...difference of its distances from the equal sides is constant. 24. The sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is equal to the perpendicular drawn from any one of the angular points to the opposite side, and is therefore... | |
 | George Albert Wentworth - 1896 - 296 σελίδες
...is common. .-. A PBD = A PEG. .: PD = BG. PE= GF. .: PD + PE= BG + GF= BF. (g 148) (g 180) Ex. 74. The sum of the perpendiculars dropped from any point...three sides is constant, and equal to the altitude. Let ABC be an equilateral A, BC the base, AD the altitude, P any point within the A, PE, PF, PG _!•... | |
 | George D. Pettee - 1896 - 272 σελίδες
...parallelogram divides the parallelogram into two equivalent figures. 294. The sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. 295. The area of a triangle is equal to the product of the semiperimeter... | |
 | Joe Garner Estill - 1896 - 214 σελίδες
...triangles have the same ratio as any two homologous sides. Prove. 5. The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. Prove. Boston University, September, 1896. TIME 1 H. 80 M. [Candidates... | |
 | Webster Wells - 1898 - 264 σελίδες
...(Ex. 13, p. 173.) (Represent the diagonals by 2 a; and 2 y.) A j 43. The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. "/-'' DE 44. The longest sides of two similar polygons are 18... | |
 | George Albert Wentworth - 1899 - 278 σελίδες
...(Why ?) .'. GF = PE. It remains to prove GB = PD. The rt. A PGB = the rt. A BDP. (Why ?) , — j£ "B Ex. 61. The sum of the perpendiculars dropped from...62. ABC and ABD are two triangles on the same base D AB, and on the same side of it, the vertex of each triangle being without the other. If AC equals... | |
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The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude. 
