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Using Proportions
with
Similar Figures
These figures are congruent. They have the
same shape and the same size.
These shapes are similar. ( )
They have the same shape, different size, the
angles are congruent and the corresponding
sides are proportional.
Corresponding sides and
corresponding angles are found in
the exact same location but on a
different shape.
If triangle ABC and triangle DEF are similar…
Let’s find corresponding sides and angles. Remember…exact same
location…but on a different shape.
D
Which angle corresponds with:
A
A
E
F
B
C
B
C
Ok…which side corresponds with:
AB
BC
CA
A
D
E
B
C
F
Since similar figures are proportional, we can use
proportions and proportion tables to prove if
corresponding sides have equal ratios.
ABC
Process
DEF
Be careful!!! Sometimes the figures may have a different
orientation (they may be turned a different way). You must be sure
to match corresponding sides. (Long side with long side…short side
with short side)
A
E
F
B
C
D
Matching corresponding sides just means you are going to
match the long side of one figure with the long side on the
other figure, and so on.
A
D
E
B
C
F
Use a table to see if the two triangles are similar.
Remember…if the ratios are equal, the shapes are similar.
A
ABC
DEF
D
12cm
8cm
48cm
24cm
B
C
6cm
E
32cm
F
Are the following shapes similar?
30
5
4
24
48
4
16
10
Here is one more way to find corresponding sides and
angles…
Look at the way they are listed in the problem