Corresponding Parts of Similar Triangles If triangles are similar are other things similar as well

Proportional Parts Conjecture If two triangles are similar, then the length of the corresponding altitudes, medians, and angle bisectors are proportional to the lengths of the corresponding sides. This shows similar Triangles

Medians with same scale factor Angles bisectors with same scale factor

Altitudes with same scale factor

Example

Angle Bisector and Opposite Side Conjecture A bisector of an angle in a triangle divides the opposite side into two segments whose lengths are in the same ratio as the lengths of the two sides forming the angle.

Example 2

More Corresponding Info Relating Perimeter, Area and Volume Remember Main shapes and how to calculate each of these Triangle Square Rectangle

Example

Continued

Triangles Relationships Given these two triangles are similar Find the scale factor – simplify fraction Find the perimeter – simplify fraction Find the area – simplify fraction What do you notice

Relationships between SF – P – A -V Scale factor = Ratio of Perimeter Scale factor squared = Ratio of Areas Scale factor cubed= Ratio of Volumes Think of the unit in the measurement and that is what you do to the scale factor.

Example If we know the scale factor of two figures is ¾ and the area of the smaller figure is 36 cm square, what is the area of the larger figure.

Homework Page 605 1-13 odd Set up proportions and solve for missing measurement