http://www.ck12.org Chapter 7. Similarity
These polygons arenot similar:
Think about similar polygons as enlarging or shrinking the same shape. The symbol∼is used to represent similarity.
Specific types of triangles, quadrilaterals, and polygons will always be similar. For example,all equilateral triangles
are similarandall squares are similar.If two polygons are similar, we know the lengths of corresponding sides are
proportional. In similar polygons, the ratio of one side of a polygon to the corresponding side of the other is called
thescale factor. The ratio of all parts of a polygon (including the perimeters, diagonals, medians, midsegments,
altitudes) is the same as the ratio of the sides.
Example A
Suppose 4 ABC∼ 4JKL. Based on the similarity statement, which angles are congruent and which sides are
proportional?
Just like in a congruence statement, the congruent angles line up within the similarity statement. So,^6 A∼=^6 J,^6 B∼=
(^6) K,and (^6) C∼= (^6) L. Write the sides in a proportion: ABJK=BCKL=ACJL. Note that the proportion could be written in
different ways. For example,ABBC=KLJKis also true.
Example B
MNPQ∼RST U. What are the values ofx,yandz?
In the similarity statement,^6 M∼=^6 R, soz= 115 ◦. Forxandy, set up proportions.
18
30
=
x
2518
30
=
15
y
450 = 30 x 18 y= 450
x= 15 y= 25