Congruent Triangles

Front

What are congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the acronym AAS stand for in triangle congruence?

Back

Angle-Angle-Side; a postulate that states if two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, then the triangles are congruent.

Front

What is the significance of the SSA condition in triangle congruence?

Back

SSA (Side-Side-Angle) is not a valid criterion for proving triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

What does AAA stand for and why is it not a valid method for proving triangle congruence?

Back

Angle-Angle-Angle; it is not valid because it only shows that triangles are similar, not necessarily congruent.

Front

What is CPCTC and how is it used in triangle congruence?

Back

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent; it is used after proving two triangles are congruent to state that their corresponding parts are also congruent.

Front

What is the SSS postulate in triangle congruence?

Back

Side-Side-Side; a postulate that states if all three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

Front

What is the SAS postulate in triangle congruence?

Back

Side-Angle-Side; a postulate that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the difference between congruent and similar triangles?

Back

Congruent triangles have the same size and shape, while similar triangles have the same shape but may differ in size.

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is fundamental in proving properties of geometric figures, solving problems, and establishing relationships between different shapes.

Front

What is the definition of an included angle in a triangle?

Back

The angle formed between two sides of a triangle.