Geometry – Triangle Congruence and Similarity

In this lesson we will learn:
Similarity: When they have the same shape, but different sizes
Similar ratios: Use similarity to find unknown side lengths!
SSS Postulate: Using sides to see if triangles are congruent
SAS Postulate: Congruence check using two sides and the angle between
ASA Postulate: Congruence check using two angles and the side between
AAS Postulate: The final congruence check for triangles
AA Postulate (Similarity): Triangles are similar when they have matching angles
SSA (ambiguous case): Depending on the sides, you can have 0, 1, or 2 triangles!

Shapes are congruent if you can turn one into the other by moving, rotating, or flipping.

Shapes are similar if you can turn one into the other by moving, rotating, flipping, or scaling.

Side-side-side postulate (SSS). If triangles have three matching side lengths, then they must be congruent.

Side-Angle-Side Postulate (SAS), if triangles have matching side-angle-side, then they must be congruent.

Angle-Side-Angle Postulate (ASA), if triangles have matching angle-side-angle, then they must be congruent.

Triangles with three matching pairs of angles are always similar.

Angle-Angle Postulate (AA), triangles with two matching pairs of angles are always similar.

Angle-Angle-Side Postulate (AAS), if triangles have matching angle-angle-side, then they must be congruent.

Geometry – Triangle Congruence and Similarity – Similarity | Similar ratios | SSS Postulate: 

Geometry – Triangle Congruence and Similarity – SAS Postulate | ASA Postulate: 

Geometry – Triangle Congruence and Similarity – AAS Postulate | AA Postulate: 

Geometry – Triangle Congruence and Similarity – SSA (ambiguous case):