If the lines _a b_, _e f_, were made longer, would their direction be changed? Then would there be any greater or less difference of direction? Then would the angles formed by them be any greater or less? Then does the _size_ of an angle depend upon the length of the lines that form it? If the lines _a b_, _e f_, were shortened, would the angle formed by them be any smaller? If two lines form an angle with each other, and meet, the point of meeting is called the vertex. What is the vertex of the angle formed by the lines _k j_, _i j_?—_i j_, _i l_? An angle is named by three letters, that which denotes the vertex being in the middle. Thus, the angle formed by _k j_, _i j_, is read _k j i_, or _i j k_. Read the four angles formed by the lines _m n_ and _o p_. The eight formed by _r s_, _t u_, and _v w_. LESSON SIXTH. REVIEW. Read all the lines that form angles with the line _a b_. (DIAGRAM 6.) Which of them forms the greatest angle with it? [Illustration: Diagram 6.] Which the least? Of the two lines _c d_, _g h_, which forms the greater angle with _e f_? Read all the angles whose vertices are at _o_ on _i j_. Which angle is the greater, _l o m_, or _m o j_?—_i o k_, or _i o l_?—_l o j_, or _m o j_? Read all the angles formed by the lines _v w_ and _x y_. Read all the angles above the line _n p_. Below the line _n p_. Above the line _q r_. At the right of the line 5 _u_. At the left. At the right of the line _s t_. At the left of the line _s t_. Which angle is the greater, _n_ 1 3, or _n_ 2 4? If the lines _x y_ and _v w_ were lengthened or produced, would the angles _v z x_, _y z w_ be any greater? If they were shortened, would the angles be any less? What is an angle? Does the size of an angle depend upon the length of the lines which form it? [Illustration: Diagram 7.] LESSON SEVENTH. RELATIONS OF ANGLES. ADJACENT ANGLES. Are the angles _a e c_, _c e b_ (DIAGRAM 7.), on the same side of any line? What line? By what other straight line are they both formed? Then, because they are both on the same side of the same straight line _a b_, and are both formed by the second straight line _c d_, they are called “_adjacent angles_.” The angles _c e b_, _b e d_ are both on the same side of what straight line? They are both formed by what second straight line? Then what kind of angles are they? Why are they called adjacent angles? Read the adjacent angles below the line _a b_. Below the line _c d_. How many pairs of adjacent angles can be formed by two straight lines? Read all the adjacent angles formed by the lines _l m_ and _n p_. VERTICAL ANGLES.