 | University of Madras - 1879 - 674 pages
...angles opposite to the equal sides equal and the areas equal, they shall be equal in all respects. IX. If a line be drawn parallel to the base of a triangle, it cuts the sides proportionally. P, Q are points in the sides CB, CA of a triangle such that BP is... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...the triangle (V. 1, Cor. 2). 2. Two squares are to each other as the squares of their diagonals. 3. If a line be drawn parallel to the base of a triangle, all lines from the vertex to the base will be cut proportionally; and the segments of the base and... | |
 | Euclides - 1884 - 434 pages
...Find the locus of the intersection of the diagonals of every ||m thus formed. 17. Straight lines are drawn parallel to the base of a triangle, to meet the sides or the sides produced. Find the locus of their middle poiuts. 18. Find the locus of the angular point... | |
 | New York (State). Department of Public Instruction - 1887 - 268 pages
...theorem: — "In an isosceles triangle the angles opposite the equal sides are «qual." 6. Demonstrate the theorem : — " If a line be drawn parallel to the base of a triangle, it will divide the .other two sides proportionally." 7. Demonstrate the theorem : — " An angle at... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 204 pages
...a series of parallel transversals, the parts thus intercepted by the latter form a proportion. 320. If a line be drawn parallel to the base of a triangle, and another from vertex to base, the parts of both the base and its parallel will form a proportion.... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...170.) Therefore Note. — Compare this demonstration with that of Prop. XIX, Chap. II. 227. COROLLARY. If a line be drawn parallel to the base of a triangle, one side is to either of its segments as the other side is to its corresponding segment. SUG. Take... | |
 | Frank Castle - Mathematics - 1899 - 424 pages
...equal to one another. Prove this by joining points DA, and AC to different points on the circumference. If a line be drawn parallel to the base of a triangle, cutting the side or sides produced, the segments of the sides are proportional. Draw a triangle ABC,... | |
 | Josiah Willard Gibbs, Edwin Bidwell Wilson - Vector analysis - 1901 - 468 pages
...lines and planes, and geometric nets in two and three dimensions are taken up in order. Example 1: If a line be drawn parallel to the base of a triangle, the line which joins the opposite vertex to the intersection of the diagonals of the trapezoid thus... | |
 | De Volson Wood - Mechanics - 1903 - 404 pages
...uniform weight ; and hence, the centre of gravity will be at the middle point of the line. EXAMPLES. 1. If a line be drawn parallel to the base of a triangle, dividing it into equal areas, will it pass through the centre of gravity of the triangle ? 2. If a... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...Ex. 51. In the figure for Ex. 50, if AD intersects CE at 0, prove A AEO is similar to A CDO. Ex. 52. If a line be drawn parallel to the base of a triangle intersecting the other two sides, the triangle formed is similar to the given triangle. 278. Homologous... | |
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ABC be a triangle, and DE a straight line drawn parallel to the base BC ; then will AD : DB : : AE : EC. 
