5.5 Proving Triangles Congruent

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What is the SSS (Side-Side-Side) Congruence Postulate?

Back

The SSS Congruence Postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What is the SAS (Side-Angle-Side) Congruence Postulate?

Back

The SAS Congruence Postulate states that 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 ASA (Angle-Side-Angle) Congruence Postulate?

Back

The ASA Congruence Postulate states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the AAS (Angle-Angle-Side) Congruence Theorem?

Back

The AAS Congruence Theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the AAA (Angle-Angle-Angle) condition?

Back

The AAA condition states that if all three angles of one triangle are equal to all three angles of another triangle, the triangles are similar but not necessarily congruent.

Front

What is the SSA (Side-Side-Angle) condition?

Back

The SSA condition does not guarantee triangle congruence; it can lead to ambiguous cases where two different triangles can be formed.

Front

If ∆ABC≅∆XYZ, what can be concluded about the corresponding sides?

Back

If ∆ABC≅∆XYZ, then AB≅XY, BC≅YZ, and AC≅XZ.

Front

What is the definition of corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the sides and angles that are equal in measure between the two triangles.

Front

What is the importance of proving triangles congruent in geometry?

Back

Proving triangles congruent is important because it allows us to establish relationships between different geometric figures and solve for unknown lengths and angles.