Triangle Congruence

Front

What is the SSS Postulate?

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 is the SAS Postulate?

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 is the ASA Postulate?

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 is the AAS Theorem?

Back

The AAS (Angle-Angle-Side) 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 two triangles are congruent.

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

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

Back

No, knowing only one side is not sufficient to determine congruence; at least two sides and the included angle or two angles and a side are needed.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.

Front

How can you prove triangles are congruent using the SSS Postulate?

Back

Measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent by SSS.

Front

What is an example of using the SAS Postulate?

Back

If triangle ABC has sides AB = 5 cm, AC = 7 cm, and angle A = 60 degrees, and triangle DEF has sides DE = 5 cm, DF = 7 cm, and angle D = 60 degrees, then triangles ABC and DEF are congruent by SAS.

Front

What is an example of using the ASA Postulate?

Back

If triangle GHI has angles G = 50 degrees, H = 60 degrees, and side GH = 8 cm, and triangle JKL has angles J = 50 degrees, K = 60 degrees, and side JK = 8 cm, then triangles GHI and JKL are congruent by ASA.