Congruent Triangles
Two triangles are congruent if they have the same shape and size. This means their
corresponding sides and angles are exactly equal.
Conditions for Congruence
To prove two triangles are congruent, one of the following conditions must be satisfied:
1. SSS (Side-Side-Side)
o
All three corresponding sides are equal.
2. SAS (Side-Angle-Side)
o
Two corresponding sides are equal, and the angle between them is also
equal.
3. ASA (Angle-Side-Angle)
o
Two corresponding angles are equal, and the side between them is also
equal.
4. AAS (Angle-Angle-Side)
o
Two corresponding angles are equal, and a non-included side is also equal.
5. RHS (Right angle-Hypotenuse-Side)
o
The hypotenuse and one other side of two right-angled triangles are equal.
How to Identify Congruent Triangles?

Look for given equal sides and angles in the diagram.

Use one of the five rules above.

If the conditions match, the triangles are congruent.
Similar Triangles
Two triangles are similar if they have the same shape but not necessarily the same size.
This means that their corresponding angles are equal, and their corresponding sides are
in proportion.
Conditions for Similarity
To prove two triangles are similar, one of these conditions must be satisfied:
1. AAA (Angle-Angle-Angle)
o
All three corresponding angles are equal.
2. SAS (Side-Angle-Side)
o
Two corresponding sides are in the same ratio, and the included angle is
equal.
3. SSS (Side-Side-Side)
o
All three corresponding sides are in the same ratio.
.
How to Identify Similar Triangles?

Check if corresponding angles are equal.

Compare the ratios of corresponding sides.

If the conditions match, the triangles are similar.
Congruence and Similarity in Other Shapes


Congruent Shapes:
o
Same in size and shape.
o
Identified by measuring sides and angles or through transformations like
rotation, reflection, or translation.
Similar Shapes:
o
Same proportions but different sizes.
o
Identified by checking if corresponding angles are equal and sides are
proportional.