7.5. Proportionality Relationships http://www.ck12.org
Triangle Proportionality
Think about a midsegment of a triangle. A midsegment is parallel to one side of a triangle and divides the other two
sides into congruent halves. The midsegment divides those two sidesproportionally.
Example 1:A triangle with its midsegment is drawn below. What is the ratio that the midsegment divides the sides
into?
Solution:The midsegment’s endpoints are the midpoints of the two sides it connects. The midpoints split the sides
evenly. Therefore, the ratio would bea:aorb:b. Both of these reduce to 1:1.
The midsegment divides the two sides of the triangle proportionally, but what about other segments?
Investigation 7-4: Triangle Proportionality
Tools Needed: pencil, paper, ruler
- Draw 4 ABC. Label the vertices.
- DrawXYso thatXis onABandYis onBC.XandYcan beanywhereon these sides.
- Is 4 X BY∼4ABC? Why or why not? MeasureAX,X B,BY,andY C. Then set up the ratiosAXX BandY CY B. Are
they equal? - Draw a second triangle, 4 DEF. Label the vertices.
- DrawXYso thatXis onDEandYis onEFANDXY||DF.
- Is 4 X EY∼4DEF? Why or why not? MeasureDX,X E,EY,andY F. Then set up the ratiosDXX EandY EFY. Are
they equal?