similar triangles PowerPoint presentationpt

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

2. The concept of similarity bears close
resemblance to the concept of congruence.
Congruent figures are exact replicas of each
other. They have the same shape and the
same size. Now consider figures that have
the same shape but not the same size. Such
figures look ‘similar’ but in essence
proportionate to each other.

3. Objects that have the same shape, but do not
have the same size, are said to be similar.
The cat on the right
is an enlargement of
the cat on the left. 
They are exactly the
same shape, but they
are NOT the same
size. These cats are
similar figures.

4. oThe The
mathematical mathematical
symbol used to symbol used to
denote similar denote similar
isis
~ .~ .
oDo you Do you
remember remember
this symbol as this symbol as
“part” of the “part” of the
symbol for symbol for
congruent??congruent??

5. In Mathematics, polygons are similar if their
corresponding (matching) angles are equal and
the ratio of their corresponding sides are in
proportion.

Facts about similar triangles:
~
~
~

6. Illustrative ExampleIllustrative Example
ABC ABC ~ DEF~ DEF
Find the value of x and y.Find the value of x and y.
Solution:
Since the corresponding sides are in proportion:
AB BC AC
DE EF DF
3/x = 4/8 = 5/y 3/x = 1/2 ; ½ = 5/y
3/x = 1/2 = 5/y x = 6 ; y = 10

7. If two triangles are similar, the ratio of the
lengths of two corresponding sides is
called the SCALE FACTOR. The scale
factor of ∆ABC to ∆DEF is 5/10 or ½.
In the same manner, the scale factor of
∆DEF to ∆ABC is 10/5 or 2/1.
Notice also that the ratio of the perimeter
P of these two triangles is equal to the
scale factor. Thus,
P of ∆DEF 10+8+6 24 2
P of ∆ABC 5+4+3 12 1

8. http://regentsprep.org/Regents/ math
/ similar/Lsimilar.htm
http://www.astro.washington.edu/
astro211/webwork3/simtri.html