TRIAL BY BATTLE 



5876 



TRIANGLE 



battery are examples of trespass to the person. 

 Poaching is a popular term for trespass upon 

 land for the purpose of obtaining game and 

 fish. Action for damages in cases of trespass 

 comes under the head of torts. See TORT. 



TRIAL BY BATTLE. See BATTLE, TRIAL BY. 



TRIANGLE, tri'angg'l, a plane figure 

 bounded by three straight sides. Triangles are 

 classified according to their sides, and according 

 to their angles. One whose three sides are 

 equal is an equilateral triangle; one which has 

 two sides equal is an isosceles triangle ; one that 

 has no two sides equal is a scalene triangle. A 

 triangle that has a right angle is a right triangle; 

 one that has an obtuse angle is an obtuse tri- 

 angle; one that has all its angles acute is an 

 acute triangle. The side upon which a triangle 

 rests is called the base, the point opposite the 

 base is called the vertex. The distance from the 

 vertex to the base is called the altitude. In a 

 right triangle one of the sides is the altitude; 

 the side opposite the right angle is called the 

 hypotenuse. 



Construction of Triangles. To the young 

 student the construction of triangles leads to 

 many interesting and valuable discoveries. He 

 finds he cannot have a triangle with any an- 

 gles he chooses, but only angles whose sum 

 is 180 ; he can have but one right angle or 

 but one obtuse angle in a triangle; he finds that 

 he can choose the size of two angles, but the 

 third one is determined for him; he finds he 

 can decide upon a certain number of sides and 

 angles, and the remaining sides and angles are 

 thereby determined. Such construction work 

 can be done with much interest and economy in 

 the sixth, seventh and eighth grades. Indeed, 

 the very keenest interest in it is found in the 

 sixth grade. It opens the way to the more ab- 

 stract demonstrative geometry of high school. 

 The student should have a rule, a compass and 

 a protractor for this work. Below are a few 

 suggestions as to problems for the student: 



1. Construct a triangle with a base of 8 inches, 

 one base angle 50 and the other 70. Can you 

 make the other two sides of the triangle any 

 length you please? Can you make the third angle 

 any size you please? 



See that one side and the two adjacent angles 

 determine the triangle. 



2. Construct a triangle, one side 10 inches, an- 

 other side 6 inches and the angle included be- 

 tween these sides 60. What do you find about 

 the third side and the other two angles? Did 

 you choose their length or size? 



See here another geometric truth two sides 

 and the included angle determine a triangle. 



3. Draw a right^ triangle ; note the position of 

 the sides. The longest side is opposite the right 



angle. Draw an obtuse triangle/" Where is the 

 longest side? In each triangle you have drawn, 

 where is the longer side? 



See that these longer sides are opposite larger 

 angles. 



4. Draw an equilateral triangle. Draw one side 

 any length ; letter the line a at one end, & at the 

 other. Take compass and with a as a center, and 

 the radius ob, draw an arc; with 6 as a center, 

 and the same radius draw another arc. Letter 

 the point where the arcs intersect c. Draw 

 straight lines from c to a and c to b. Measure 

 the angles of this triangle. What do you find? 



5. Repeat Problem 4 but change length of first 

 side. 



The Pythagorean Theorem. The relation of 

 the sides of a right triangle has been known 

 for many centuries. Pythagoras proved, about 

 500 B. c., that the square on the hypotenuse of 

 a right triangle is equal to the sum of the 

 squares on the other two sides. 



Draw a right triangle, a b c, base 3 inches and 

 altitude 4 inches. Measure the third side, the 

 hypotenuse. 



Draw a square on the base line, draw a square 

 on the altitude line, draw a square on the hypote- 



ILLUSTRATING THE PYTHAGOREAN 

 THEOREM 



nuse. How does the square on the hypotenuse 

 compare with the other two squares? 



Draw other right triangles and build squares 

 on the sides. How does the square upon the 

 hypotenuse compare with the other two squares 

 in each case? The general truth is stated: 

 Hypotenuses = Base2 + Altitudes 



From this fact, any side of a right triangle 

 may be found when the other two sides are 

 known. 



Problems. 1. What is the diagonal of a 

 rectangular field 60 rods by 80 rods? 



Solution : 



H2=3600 + 6400 



