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CHAPTER 7
SIMILAR
POLYGONS
SECTION 7-1
Ratios and Proportions
RATIO – a comparison of
two numbers, a and b,
represented in one of the
following ways:
a:b
a or a to b
b
EQUIVALENT RATIOS –
two ratios that can both be
named by the same fraction.
4:8
and 7 :14
PROPORTION – is an
equation that states that
two ratios are equivalent.
a:b=c:d
a=c
b d
EXTREMES – the first and last
terms
a : b= c : d
a and d are extremes
MEANS – the second and third
terms
a:b=c:d
b and c are means
CROSS PRODUCTS – the
product of the extremes
equals the product of the
means.
ad= bc
SECTION 7-2
Properties of Proportions
TERMS – the four
numbers a, b, c, and d that
are related in the
proportion.
Properties of Proportions
a/b = c/d is equivalent to:
a) ad = bc
b) a/c = b/d
c) b/a = d/c
d) (a + b)/b = (c + d)/d
2. If a/b = c/d = e/f = …, then
(a+c+e+…)/(b+d+f+…) = a/b = …
1.
SECTION 7-3
Similar Polygons
SCALE DRAWING – is a
representation of a real
object.
SCALE – is the ratio of the
size of the drawing to the
actual size.
SIMILAR – figures that have
the same shape
CORRESPONDING ANGLES
– angles in the same
position in congruent or
similar polygons.
CORRESPONDING SIDES –
sides in the same position
in congruent or similar
polygons.
SIMILAR POLYGONS – figures
having all corresponding
angles congruent and the
measures of all
corresponding sides are in
the same proportion. The
symbol for similarity is 
Scale Factor
- The ratio of the lengths of
two corresponding sides
SECTION 7-4
A Postulate for
Similar Triangles
AA Similarity

If two angles of one
triangle are
congruent to two
angles of another
triangle, then the
triangles are similar.
SECTION 7-5
Theorems for Similar
Triangles
SAS Similarity

If an angle of one triangle is
congruent to an angle of
another triangle and the
sides including those angles
are in proportion, then the
triangles are similar.
SSS Similarity

If the sides of two triangles
are in proportion, then the
triangles are similar.
SECTION 7-6
Proportional Lengths
Theorem 7-3

If a line parallel to one side
of a triangle intersects the
other two sides, then it
divides those sides
proportionally.
Corollary

If three parallel lines
intersect two
transversals, then they
divide the transversals
proportionally.
Theorem 7-4

If a ray bisects an angle of
a triangle, then it divides
the opposite side into
segments proportional to
the other two sides.
END