Download Similar Triangles Two triangles are similar if their corresponding

Similar Triangles
Two triangles are similar if their corresponding angles are congruent and their corresponding
sides are proportional.
It is, however, not essential to prove all 3 angles of one triangle congruent to the other, or for that
matter all three sides proportional to the other. If some of these specific conditions get satisfied,
the rest, automatically, get satisfied. Those particular conditions would be enough to guarantee
similarity. These are the minimum sufficient conditions for similarity. 1) In 2 triangles if the
corresponding angles are congruent, their corresponding sides are equal.
A A (Angle-Angle): If two angles of one triangle are congruent with the corresponding two
angles of another triangle, the two triangles are similar.
***The sum of all three angles of a triangle is 180o. Therefore if two pairs of angles are
congruent, the third is automatically congruent. Therefore, the minimum sufficient condition
requires only two angles to be congruent.
S A S (Side-Angle-Side): If two sides of one triangle are proportionate to the two corresponding
sides of the second triangle and the angles between the two sides of each triangle are equal the
two triangles are similar.
S S S (Side-Side-Side): If the three sides of one triangle are proportional to the three
corresponding sides of another triangle, then the two triangles are similar.
Example 1
 ABC and  DEF have a one to one correspondence such that
.
Solution:
Are the two triangles similar ? If so, why ?
Yes. The two triangles are similar because their corresponding sides are proportionate.
Example
a)
b)
c)
Each pair of triangles is similar. Which minimum sufficient conditions would prove they are
similar?