Dividing a Segment Proportionately

Instruction

First, explore the GeoGebra applet and then try to answer the questions below. [br]To do this, follow the construction steps 1 to 4 and read the instructions carefully. [br][br]You can change the task by draging the sliders below and modifying the proportional ratio m : n. [br]Move point B and check whether the given ratio is still valid.

Which statements are accurate to divide a segment propotionately?

It does not matter how many parts the auxiliary line has. The division of a segment propotionately can only be done graphically and can not be calculated. If the ratio is 3 : 4, the 7th auxiliary point is connected to the end of the segment and the parallel line through the 3rd point gives the correct division on the given segment. To divide a segment you have to add the ratios and then divide the auxiliary segment into as many equal parts as the value of the sum.

Task

Now use your workbook and divide the segments into the given proportion graphically:[br][list=1][*]Divide the segment AB = 10 cm into the proportion 2 : 4.[/*][*]Divide the segment EF = 12 cm into the proportion 3 : 5.[/*][*]Divide the segment XY = 15 cm into the proportion 5 : 6.[/*][/list]Check your solution by calculating and measuring the length of the divided segments!

Dividing a Segment Proportionately

Instruction

Which statements are accurate to divide a segment propotionately?

Task

Information: Dividing a Segment Proportionately