SECOND LESSON. (Each of the Definitions should be illustrated by the Teacher.) 1. An angle is the corner formed by the union of two lines proceeding in different directions. 2. Rectilinear angles are formed by right lines. 3. Rectilinear angles are either right, obtuse, or acute. 4. A right angle is formed by one line falling on another perpendicularly. 5. An obtuse or blunt angle is greater than a right angle. 6. An acute or sharp angle is less than a right angle. EXERCISES. Look round the room, and show me a right angle. An obtuse. An acute. What angle does the lid of the slanting desk make with the table? The corner of the room with the ceiling, &c. &c.? Draw a right angle of 6 inch lines. (Fig. 8.) An obtuse angle same size. (Fig. 9.) An acute angle of 8 inch lines. (Fig. 10.) Draw a horizontal line any length; place a perpendicular at one end, and an oblique line running inwards at the other. (Fig. 11.) Angles thus formed? Draw a similar angle to those made by the walls and ceiling. A similar one to a ladder leaning against a wall. Explain it. Draw two acute angles, one within the other, 1 inch apart, the longer one of 12 inch lines. (Fig. 12.) Draw a 12 inch perpen. dicular, and a 6 inch horizontal, exactly intersecting. (Fig. 13.) Explain the angles. Draw a large angle in the form of a V. Explain it. Draw two oblique 6 inch lines cutting each other in the centre. (Fig. 14.) Number and kinds of angles? Repeat the two last exercises in one figure. (Fig. 15.) Analyse and explain the angles. Which is the larger, an acute angle formed of 20 inch lines, or a right angle of 6 inch lines? See Appendix, B. B THIRD LESSON. DEFINITIONS. (Illustrate on black board.) 1. A square is a four-sided figure with all its sides equal and all its angles right angles. 2. An oblong, parallelogram, or rectangle, has its two opposite sides equal, and its angles right angles. 3. The area or superficies of a figure is the surface enclosed by the sides. 4. A diagonal is a line running from the opposite corner of a four-sided figure. 5. Figures with four sides are called quadrilateral. EXERCISES. What form is this room? These books? The window? The door? Point out a square. A parallelogram. Where would a diagonal be drawn across this room? Draw a diagonal across your board. Draw a 9 inch square. (Fig. 16.) Draw a rectangle 12 inches by 6. Divide it into two squares. Add diagonals. (Fig. 17.) Draw an 8 inch square. Add two diagonals, and a perpendicular, and horizontal line. (Fig. 18.) What angles made by these? Draw a rectangle 12 inches by 4 inches. Divide it into three squares. (Fig. 19.) Copy Exercise 20, making the squares 4, 3, 2, and 1 inch respectively. Copy Exercise 21, the same proportion as the last. See Appendix, C. |