9.46 Chapter 9
Think
Susan's conclusion is not true. Why?
More about the Properties of Similar Figures
In fact, for similar polygons, all their corresponding lengths
(e.g. bases, heights, diagonals) are proportional.
e.g. For similar parallelograms X and Y on the right,
a1 and a2 are their corresponding bases,
h1 and h2 are their corresponding heights,
k1 and k2 are their corresponding diagonals.
We have 2
1
a
a = 2
1
h
h = 2
1
k
k , i.e. their corresponding lengths
are proportional.
Likewise, for similar figures involving curves such as circles
and semi-circles, their corresponding lengths (e.g. diameters, perimeters)
are also proportional.
e.g. For similar semi-circles F and G on the right,
d1 and d2 are their diameters,
s1 and s2 are their perimeters.
We have 2
1
d
d = 2
1
s
s , i.e. their corresponding lengths
are proportional.
k1
a1
k2
h2
h1
a2
parallelogram X
k1
a1
k2
h2
h1
a2
parallelogram Y
semi-circle F semi-circle G
d1
s1
d2
s2
A P S
D E M N
B C Q R
The three interior angles of
3ABC are equal to those of
3ADE. Hence, 3ABC and
3ADE are similar triangles.
Kelvin
The four interior angles
of PQRS are equal to
those of PMNS. Hence,
PQRS and PMNS are
similar figures.
Susan