**Problem : **
If triangle ABC is similar to triangle DEF, which side is proportional to side BC?

Side EF.

**Problem : **
Triangles ABC and DEC are similar, and line *l* is parallel to segment AB. What
is the length of CE?

8

**Problem : **
Can two triangles be similar but not congruent? Can they be congruent but not similar?

Every pair of congruent triangles are similar, but every pair of similar triangles isn't
necessarily congruent.

**Problem : **
When a line is drawn through an equilateral triangle such that it is parallel to one side and
intersects one time with each of the other two sides, how many similar pairs of triangles
are created?

Thirty-six. If the equilateral triangle is triangle ABC, and the line intersects with sides
AC and BC, then a new triangle, DFC, is created. Let point D be the intersection point of
the line and side AC and let point E be the intersection point of side BC. Then triangle
DFC is similar to triangles ABC, BCA, CAB, ACB, BAC, and CBA. The five other
triangles, FCD, CDF, DCF, FDC, and CFD are also all similar to these six triangles,
making 36 pairs of similar triangles.