 The sum of the perpendiculars dropped from any point in the base of an isosceles triangle to the legs, is equal to the altitude upon one of the arms.  Plane and Solid Geometry - Page 71by George Albert Wentworth - 1899 - 473 pagesFull view - About this book
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...inscribed circle taken as often as the figure has sides. Cor. 3. The sum of the two perpendiculars drawn from any point in the base of an isosceles triangle to the other sides, is equal to the sum of those drawn from any other point in the base to those sides, or... | |
 | Euclides - 1883 - 176 pages
...given point to draw a line equally inclined to two given lines. 161. The sum of the perpendiculars from any point in the base of an isosceles triangle to the other sides is the same whatever point be taken. When the point is in the base produced, sum changes... | |
 | Euclides - 1884 - 434 pages
...is constant, the isosceles triangle has the least perimeter. 13. The sum of the perpendiculars drawn from any point in the base of an isosceles triangle to the other two sides is constant. Examine the case when the point is in the base produced. 14. The sum of... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...parallel to the sides of the given parallelogram. IX. THEOREM. — Show that the sum of the distances from any point in the base of an isosceles triangle to the two other sides, is equal to the distance from the vertex of either angle at the base to the opposite... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...acute angles of a right triangle is double the other, the hypotenuse is double the shortest side. 73. The sum of the perpendiculars dropped from any point...constant, and equal to the altitude upon one of the legs. HINT. Let PD and PE be the two Js, BF the altitude upon AC. Draw PG ± to BF, and prove the A PBO and... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...acute angles of a right triangle is double the other, the hypotenuse is double the shortest side. 73. The sum of the perpendiculars dropped from any point...of an isosceles triangle to the legs is constant, o and equal to the altitude upon one of the legs. HINT. Let PD and PE be the two Js, BF the altitude... | |
 | George Albert Wentworth - 1889 - 276 pages
...perimeter equal to the sum of the legs of the triangle. 17. The sum of the perpendiculars dropped from a point in the base of an isosceles triangle to the legs is constant and equal to the altitude upon a leg. c Fig. I. Fig. 2. Let (Fig. l) PD and PE be the two perpendiculars, BF the altitude upon the... | |
 | George Albert Wentworth - 1889 - 264 pages
...perimeter equal to the sum of the legs of the triangle. 17. The sum of the perpendiculars dropped from a point in the base of an isosceles triangle to the legs is constant and equal to the altitude upon a leg. Fig. I. Fig. 2. Let (Fig. l) PD and PE be the two perpendiculars, BF the altitude upon the leg... | |
 | George Cunningham Edwards - Geometry - 1895 - 330 pages
...bisected, and a line DE be drawn through I, \\ to AB, DE = AD + BE. 14. The sum of the perpendiculars from any point in the base of an isosceles triangle to the equal sides is constant, and equals the altitude from one of the equal angles. FIG. 17T. Proof. —AK... | |
 | George Albert Wentworth - Geometry - 1896 - 296 pages
...(2), CB=CE= AE. That is, CB = J (M, ~-D (§ 143) (? 157) (1) (2) PLANE GEOMETRY. — BOOK I. Ex. 73. The sum of the perpendiculars dropped from any point...and equal to the altitude upon one of the legs. Let ABC be an isosceles A, AB the base, P any point in AB, PD -L to BC, P£_L to AC, and draw BF ± to... | |
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