 The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.  Plane Geometry - Page 71by George Albert Wentworth - 1899 - 256 pagesFull view - About this book
 | Levi Leonard Conant - Geometry - 1905 - 134 pages
...intersection of the diagonals, and also through the intersection of the non-parallel sides produced. 61. The sum of the perpendiculars dropped from any point within an equilateral triangle upon the three sides is constant. To what is it equal ? What if the point be without the triangle?... | |
 | University of Mississippi - 1905 - 262 pages
...included angle of the one arc equal, respectively, to two sides and the included angle of the other. 2. The sum of the perpendiculars dropped from any point within an equilateral triangle is equal to the altitude. 3. To construct a triangle when two sides and the angle opposite one of them... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...prove PH — PK = CD, a constant. Proof same as in Ex. 200.] 202 The sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is constant. [Draw MPN II to BC. By Ex. 200, PH + PK = AE. . -. PH -f PK + PL = AD, an altitude and .-. a constant.]... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...point of the base.) [Prove PE = CF by 184 (1).] * PC 150. The sum of the three perpendiculars drawn from any point within an equilateral triangle, to the three sides, is constant for all positions of the point. [Draw a line through this point II to one side; draw the altitude of... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...prove PH — PK = CD, a constant. Proof same as in Ex. 200.] 202 The sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is constant. [Draw MPN II to BC. By Ex. 200, PH -f PK = AE. . •. PH + PK + PL = AD, an altitude and . •. a constant.... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...point of the base.) [Prove PE = CF by 184 (1).] * PC 150. The sum of the three perpendiculars drawn from any point within an equilateral triangle, to the three sides, is constant for all positions of the point. [Draw a line through this point II to one side; draw the altitude of... | |
 | Henry Sinclair Hall - 1908 - 286 pages
...modified if the given point were taken in the base produced ? 15. 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... | |
 | Geometry, Plane - 1911 - 192 pages
...each other as the products of the sides including the equal angles. 7. The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. 8. Two regular polygons of the same number of sides are similar.... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...to the legs is equal to the altitude upon one of the legs (Fig. 1). 3. 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. 2). 4. If two medians of a triangle are equal, the triangle... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...to the legs is equal to the altitude upon one of the legs (Fig. 1). 3. 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. 2). 4. If two medians of a triangle are equal, the triangle... | |
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