Dividing a line segment
Draw AB = 7 cm and divide it into 3 equal parts.
Draw AB = 8 cm and divide it into 5 equal parts.
Draw AB = 6.5 cm and divide it into 4 equal parts.
Draw AB = 7.5 cm and divide it at P so that AP : PB = 2 : 3.
Draw AB = 7 cm and divide it at P so that AP : PB = 3 : 4.
1. Draw AB = 7 cm.
2. From A, draw a ray AX below AB, at any acute angle to it.
3. With A as the center and any radius (here 1.2 cm), cut AX at C. With C as the center and the same radius, cut it at D, and so on: 3 equal steps, to E.
4. Join EB.
5. Through C and D, draw lines parallel to EB (slide a set square along a ruler). They cut AB at K and L.
6. AB is cut into 3 equal parts of 2.33 cm.
1. Draw AB = 8 cm.
2. From A, draw a ray AX below AB, at any acute angle to it.
3. With A as the center and any radius (here 1.2 cm), cut AX at C. With C as the center and the same radius, cut it at D, and so on: 5 equal steps, to G.
4. Join GB.
5. Through C, D, E and F, draw lines parallel to GB (slide a set square along a ruler). They cut AB at K, L, M and N.
6. AB is cut into 5 equal parts of 1.6 cm.
1. Draw AB = 6.5 cm.
2. From A, draw a ray AX below AB, at any acute angle to it.
3. With A as the center and any radius (here 1.2 cm), cut AX at C. With C as the center and the same radius, cut it at D, and so on: 4 equal steps, to F.
4. Join FB.
5. Through C, D and E, draw lines parallel to FB (slide a set square along a ruler). They cut AB at K, L and M.
6. AB is cut into 4 equal parts of 1.63 cm.
1. Draw AB = 7.5 cm.
2. From A, draw a ray AX below AB, at any acute angle to it.
3. With A as the center and any radius (here 1.2 cm), cut AX at C. With C as the center and the same radius, cut it at D, and so on: 5 equal steps, to G.
4. Join GB.
5. Through D, draw a line parallel to GB (slide a set square along a ruler). It cuts AB at P.
6. AP : PB = 2 : 3: AP = 3 cm and PB = 4.5 cm.
1. Draw AB = 7 cm.
2. From A, draw a ray AX below AB, at any acute angle to it.
3. With A as the center and any radius (here 1.2 cm), cut AX at C. With C as the center and the same radius, cut it at D, and so on: 7 equal steps, to J.
4. Join JB.
5. Through E, draw a line parallel to JB (slide a set square along a ruler). It cuts AB at P.
6. AP : PB = 3 : 4: AP = 3 cm and PB = 4 cm.
Why it works
The lines through the marks are parallel, and they cut AX into equal steps. A line parallel to one side of a triangle cuts the other two sides in the same ratio, so they cut AB in the same ratio as the steps along AX: equal parts, or m steps to n.