Is there a shorter way?
In the next few pages, we will explore if it is possible for us to prove that two triangles are congruent without showing that ALL the corresponding lengths and ALL the corresponding angles are equal.
We will explore the following conditions:
- SSS (Side-Side-Side): If two triangles have 3 equal corresponding sides, are they congruent?
- AAA (Angle-Angle-Angle): If two triangles have 3 equal corresponding angles, are they congruent?
- SAS (Side-included Angle-Sides): If two triangles have 2 equal corresponding sides and one equal included angle, are they congruent?
- RHS (Right angle-Hypotenuse-Side): If two right-angled triangles have equal hypotenuse and one equal corresponding sides, are they congruent?
- SSA (Side-Side-Angle): If two triangles have two equal corresponding lengths and one equal corresponding angle (which is not between the two sides), are they congruent?
-ASA (Angle-Side-Angle): If two triangles have two equal corresponding angles and one equal corresponding side (which is between the two angles), are they congruent?
-AAS (Angle-Angle-Side): If two triangles have two equal corresponding angles and one equal corresponding side (which is not between the two angles), are they congruent?