 | 1906 - 818 pages
...contained by the whole and that part, together with the square on the other part. 4. In every triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by cither of these sides,... | |
 | Trinity College (Dublin, Ireland) - 1908 - 574 pages
...the same parallels are equal in area. 5. In any triangle, prove that the square on the side opposite an acute angle is less than the sum of the squares on the sides containing the acute angle by twice the rectangle contained by one of tbe latter lines and the projection of the... | |
 | George William Myers - Mathematics - 1910 - 304 pages
...angle ABC, until it becomes acute, as in Fig. 269, we find that the square on the side opposite the acute angle is less than the sum of the squares on the other two sides. EXERCISES 1. What is the relation between a', b2, and c2 (Fig. 270) Q whenZB=o0°?... | |
 | Trinity College (Dublin, Ireland) - 1911 - 614 pages
...and between the same parallels are equal in area. 2. Prove that the square of a side of a triangle subtending an acute angle is less than the sum of the squares of the sides containing the angle by twice a certain rectangle. 3. Prove that chords nearer to the... | |
 | Alberta. Department of Education - Education - 1912 - 244 pages
...the part produced. 6 — II. 3 (b) Express the theorem in (o) algebraically. 9 10. In every triangle the square on the side subtending an acute angle is...than the sum of the squares on the sides containing the acute angle, by twice the rectangle contained by either of these sides, and the straight line intercepted... | |
 | University of Calcutta - 1912 - 746 pages
...equal, the figure is a 6 parallelogram. 8. In any triangle, the square on the side subtending an acute 8 angle is less than the sum of the squares on the sides containing that angle by twice the rectangle contained by either of these sides nnd the projection on it of the other. ABC is a triangle and D is... | |
 | University of South Africa - Universities and colleges - 1913 - 768 pages
...ab -f b2. (3) (a — b)a — a.. — 2 ah + bi. 14) 0z _ bz = (a -fb) (a — b). 1n every triangle, the square on the side subtending an acute angle is...sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let... | |
 | Newfoundland Council of Higher Education - 1913 - 228 pages
...7. Prove that, in an acute-angled triangle, the square on the ride opposite one of the acute angles is less than the sum of the squares on the sides containing that acute angle by twice the rectangle contained by one of the latter sides and the projection of the other... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...decreases, the square on AC decreases, Fig. 150. Therefore in a triangle the square on the side opposite an acute angle is less than the sum of the squares on the other two sides. In a similar way, by increasing the right angle ABC, Fig. 149, as in Fig. 151, we... | |
 | Trinity College (Dublin, Ireland) - 1917 - 560 pages
...given triangle, and have an angle equal to a given angle. 4. Prove that in any triangle the square of a side subtending an acute angle is less than the sum of the squares of the other sides by twice the rectangle contained by either of those sides, and the straight line... | |
| |
In every triangle, the square on the side subtending an acute angle is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let... 
