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Similar Triangles
Proving Triangles Similar
Same idea as polygons
Similar Triangles
Corresponding angles need to be congruent
Corresponding sides need to be proportional
All should have same scale factor
You can write 2 column proofs like before, but
we have to state sides proportional instead of
congruent.
Similar Triangles
Given two angles measures of 70 and 45, each person draw a
triangle using a protractor and straight edge – are the
triangles similar can you prove they are (definition of similar)
Give the measurements of 3 sides of a triangle as 5 cm, 8 cm
and 10 cm, construct a triangle, if you use the same scale
factor on all the sides and construct another triangle prove
they similar (def)
Given 2 sides and the included angle, 6 cm 9 cm and 65
degrees, construct a triangle, keeping the angle the same just
changes the sides with the same scale factor construct
another triangle, prove these triangles similar (def)
Proving Triangles Similar
AA – Angle Angle – if 2 corresponding angles are
congruent then the third has to be congruent
SSS – Side Side Side – all corresponding sides are
proportional, same scale factor, same decimal
SAS – Side Angle Side – if two sides of one triangle
are proportional to two corresponding sides of
another triangle and the included angle is
congruent, then the triangles are similar
Are the triangles similar. If yes then state the conjecture as
to why and state the similarity statement (can you support
the why what work or statements would you need), if no
state why not.
Example
Example
Given the Alt of a Right Triangle
E
C
B
C
E
B
E
D
C
Notice the 3 similar triangles that are formed
Can you set up proportions that relate sides of large triangle to other two
What about a proportion that relates small and medium
D
Homework
Pg 591 2-10 even and 13
State how triangles are similar