Triangle Congruency

Front

What does the SSS postulate state?

Back

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

Front

What does the SAS postulate state?

Back

The SAS (Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does the ASA postulate state?

Back

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Front

What does the AAS postulate state?

Back

The AAS (Angle-Angle-Side) postulate states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What is the definition of congruent triangles?

Back

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

Front

If ∠A ≅ ∠D, what can be inferred about triangles that include these angles?

Back

If ∠A ≅ ∠D, it indicates that the triangles containing these angles may be congruent if other conditions (like sides) are also met.

Front

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

Back

The included angle in the SAS postulate is crucial because it is the angle formed between the two sides being compared, ensuring the triangles are congruent.

Front

Can two triangles be congruent if only one side is known to be equal?

Back

No, knowing only one side is not sufficient to prove triangle congruence; at least two sides and the included angle (SAS) or two angles and a side (ASA or AAS) must be known.

Front

What is the relationship between the SSS and SAS postulates?

Back

The SSS postulate can be used to prove congruence, and if two triangles are proven congruent by SSS, they can also be proven congruent by SAS.

Front

What is a counterexample in the context of triangle congruence?

Back

A counterexample is a specific case that disproves a statement; for example, two triangles with two equal angles but different side lengths are not congruent.