Front

What does it mean for triangles to be congruent?

Back

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

Front

What is the SAS postulate?

Back

The Side-Angle-Side (SAS) 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 postulate?

Back

The Angle-Side-Angle (ASA) 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 SSS postulate?

Back

The Side-Side-Side (SSS) postulate states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What is the AAS postulate?

Back

The Angle-Angle-Side (AAS) postulate 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 does the congruency statement ∆ABC ≅ ∆DEF imply?

Back

It implies that the corresponding angles and sides of triangles ABC and DEF are equal: ∠A = ∠D, ∠B = ∠E, ∠C = ∠F and AB = DE, BC = EF, AC = DF.

Front

How does the order of letters in a congruency statement matter?

Back

The order of letters in a congruency statement indicates which angles and sides correspond to each other. For example, in ∆ABC ≅ ∆DEF, A corresponds to D, B to E, and C to F.

Front

What is the significance of the included angle in the SAS postulate?

Back

The included angle is the angle formed between the two sides being compared. It is crucial for establishing congruence in the SAS postulate.

Front

Can two triangles be congruent if only one angle and one side are known?

Back

No, at least two sides and the included angle (SAS) or two angles and the included side (ASA) must be known to establish congruence.

Front

What is the relationship between corresponding angles in congruent triangles?

Back

In congruent triangles, corresponding angles are equal.