See the attached PDF file for detailed instructions for this activity

Print pages 61 - 64 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Construct a triangle XYZ

Draw a line parallel to XZ which intersects side XY in point A and side YZ in point B

Measure XA, YA, ZB, and BY

Calculate the ratios XA / AY and ZB / BY

Observe that the ratios are same

Alter the triangle to check the relationship

Note that the ratios stay equal if the triangle is changed, but differ when the parallel line is relocated

Observe that a line parallel to one side of a triangle intersects the other two sides and divides the two sides proportionally

Construct a triangle ABC

Bisect angle ABC

Label the point of intersection of the angle bisector and side AC as Z

Measure AZ, ZC, AB, and BC

Calculate the ratios AZ / ZC and AB / BC

Observe that the ratios are equal

Observe that a line that bisects an angle of a triangle divides the opposite side into segments, which are proportional to the lengths of the other two sides

After the Activity

Review student results:

As a class, discuss questions that appeared to be more challenging