Triangle Congruence Postulates

Front

What is the AAS postulate in triangle congruence?

Back

AAS stands for Angle-Angle-Side. It 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 triangles are congruent.

Front

What does the SAS postulate state?

Back

SAS stands for Side-Angle-Side. It 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 triangles are congruent.

Front

Define the SSS postulate in triangle congruence.

Back

SSS stands for Side-Side-Side. It states that if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What is the ASA postulate?

Back

ASA stands for Angle-Side-Angle. It states that if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

Can two triangles be congruent if only two angles are known?

Back

No, knowing only two angles (AAA) does not guarantee triangle congruence, as it does not provide information about the sides.

Front

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

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

Front

How can you determine if triangles are congruent using AAS?

Back

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, the triangles are congruent by AAS.

Front

What is the relationship between the angles and sides in the ASA postulate?

Back

In the ASA postulate, two angles and the side between them (included side) must be congruent for the triangles to be congruent.

Front

Explain the SSS postulate with an example.

Back

If triangle ABC has sides AB = 5 cm, BC = 7 cm, and AC = 8 cm, and triangle DEF has sides DE = 5 cm, EF = 7 cm, and DF = 8 cm, then triangles ABC and DEF are congruent by SSS.

Front

What does it mean if two triangles are congruent?

Back

If two triangles are congruent, it means they have the same size and shape, with corresponding sides and angles being equal.