 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.  Plane and Solid Geometry - Page 71by George Albert Wentworth - 1899 - 473 pagesFull view - About this book
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...prove EFGH a parallelogram equal to one half ABCD. Ex. 22. Prove that the sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. Suggestions. — 1. ABPC+A .BP.4 + A ^PC=A ABC. 2. Express the... | |
 | William Betz - Geometry - 1916 - 536 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... | |
 | Michele Giua, Clara Giua-Lollini - Alloys - 1918 - 370 pages
...of A, 70 per cent, of B and 10 per cent, of C, if 100 be substituted for unity. If perpendiculars be dropped from any point within an equilateral triangle to the three sides the sum of the lengths of these perpendiculars is equal to the length of a perpendicular from one of... | |
 | Military Academy, West Point - 1934 - 964 pages
...its sides p and g and m the median to the third side. 10 Theorem: The sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is constant. 10 Theorem: Two diagonals of a regular pentagon, not drawn from a common verter, divide each other... | |
 | Brian S. Mitchell - Technology & Engineering - 2004 - 976 pages
...accomplished using the center of gravity rule, which states that the sum of the perpendicular distances from any point within an equilateral triangle to the...three sides is constant and equal to the altitude of the triangle. With reference to Figure 2.15, this means that the quantity (a + b + c) is a constant,... | |
 | Brian S. Mitchell - Technology & Engineering - 2003 - 982 pages
...accomplished using the center of gravity rule. which states that the sum of the perpendicular distances from any point within an equilateral triangle to the...three sides is constant and equal to the altitude of the triangle. With reference to Figure 2.15. this means that the quantity (a + b + c1 is a constanL... | |
 | 228 pages
...equal to CD. Given AB = CD = x, AC=BD=y, prove that 6. Show that the sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is the same for all positions of the point. 7. A rectangle has for one side a chord of a circle and for... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 356 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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