Triangle Congruence SSS,SAS,AAS,ASA

Front

What does the SSS postulate state?

Back

The SSS (Side-Side-Side) 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 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 equal 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 equal 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 equal to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between the two angles to be equal, while AAS does not require the side to be included between the two angles.

Front

Can SSA (Side-Side-Angle) prove triangle congruence?

Back

No, SSA does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

If two triangles have sides of lengths 5, 7, and 10, are they congruent?

Back

To determine congruence, compare with another triangle's sides. If they match, they are congruent; otherwise, they are not.

Front

How can you prove triangles are congruent using the SAS postulate?

Back

Identify two sides and the included angle of one triangle that are equal to two sides and the included angle of another triangle.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same shape and size, which allows for the transfer of properties and measurements between them.

Front

Provide an example of using the AAS postulate.

Back

If triangle ABC has angles A = 30°, B = 60° and side a = 5, and triangle DEF has angles D = 30°, E = 60° and side d = 5, then triangles ABC and DEF are congruent by AAS.