The following are several "shortcuts" to proving whether or not two triangles can be similar. Some of these shortcuts are valid, but others are invalid.[br][br]Use your knowledge of similar polygons to find the valid shortcuts. [br]Check your understanding at the bottom of this worksheet.

[br][br]If two pairs of corresponding angles in two triangles[br]are congruent, then the third angles must be congruent too. This guarantees the[br]triangles are similar.[br][br][br]

[b]Two pairs of proportional side lengths alone[/b] are [b]not[/b][br]enough to guarantee similarity.

If [b]all three pairs of corresponding sides[/b] in two[br]triangles are [b]proportional[/b], then the triangles are [b]similar[/b]. This[br]means their angles will also be equal, maintaining the same shape but different[br]sizes.[br][br][br]

In this case, we only have [b]two proportional sides and a[br]non-included angle[/b]. That’s not enough! The third angle could vary depending[br]on how the triangle is formed, meaning similarity is [b]not guaranteed.[/b][br][br][br]

[b]SAS Similarity [/b]guarantees that the triangles are similar.