Assignment 6

Examining
Similar Triangles

By
Robin Kirkham, Cara Haskins, and Matt Tumlin

** **

Let us begin
our exploration by defining similar figures. In order to prove that any two figures are similar, the measures
of corresponding angles must be the same, but the measures of corresponding
sides must be multiples (proportional) of each other.

** **

For our
example we are going to construct any triangle **ABC**:

In this
example, let the lengths of the sides of triangle **ABC** be as
follows:

m BA ~= 5 cm

m BC ~= 8 cm

m AC ~= 4 cm

Let the
measurements of the interior angles of triangle **ABC** be as
follows:

m angle ABC~= 30 degrees

m angle BAC ~= 120
degrees

m angle ACB ~= 40
degrees

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If we take
the midpoints of this triangle and construct segments from the midpoints to the
vertices, then we can copy these segments to construct a new triangle **DEF**, as noted
below:

For the new
triangle **DEF**, the lengths of the sides are as follows:

m FE ~= 3 cm

m DE ~= 6 cm

m DF ~= 2 cm

The
corresponding angles are congruent.

Therefore, these
two triangles constructed from one triangle are similar, as the sides are in
proportion and the angles are congruent.