Triangle Similarity Shortcuts
Observations and discoveries
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.
Use your knowledge of similar polygons to find the valid shortcuts.
Check your understanding at the bottom of this worksheet.
AA Shortcut Test
If two pairs of corresponding angles in two triangles
are congruent, then the third angles must be congruent too. This guarantees the
triangles are similar.
S S Shortcut Test
Two pairs of proportional side lengths alone are not
enough to guarantee similarity.
S S S Shortcut Test
If all three pairs of corresponding sides in two
triangles are proportional, then the triangles are similar. This
means their angles will also be equal, maintaining the same shape but different
sizes.
S S A Shortcut Test
In this case, we only have two proportional sides and a
non-included angle. That’s not enough! The third angle could vary depending
on how the triangle is formed, meaning similarity is not guaranteed.
S A S Shortcut Test
SAS Similarity guarantees that the triangles are similar.
Check Your Understanding
Which shortcuts did you think were valid?