4b.6 AAS Congruency Postulate

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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 is the AAS Congruency Postulate?

Back

The AAS Congruency Postulate states that if in two triangles, two angles and a side opposite one of the angles in one triangle are equal to two angles and the corresponding side in the other triangle, then the two triangles are congruent.

Front

List the triangle congruence theorems.

Back

The main triangle congruence theorems are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).

Front

What is the difference between ASA and AAS?

Back

ASA (Angle-Side-Angle) requires the side to be between the two angles, while AAS (Angle-Angle-Side) does not require the side to be between the two angles.

Front

Can AAS be used to prove triangle congruence?

Back

Yes, AAS can be used to prove triangle congruence, as it is one of the valid triangle congruence postulates.

Front

What is the SSS Congruence Postulate?

Back

The SSS Congruence 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 Congruence Postulate?

Back

The SAS Congruence 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 Congruence Postulate?

Back

The ASA Congruence Postulate states that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, then the two triangles are congruent.

Front

Provide an example of AAS in a triangle.

Back

If triangle ABC has angles A = 50° and B = 60°, and side a (opposite angle A) = 5 cm, and triangle DEF has angles D = 50° and E = 60°, and side d (opposite angle D) = 5 cm, then triangles ABC and DEF are congruent by AAS.

Front

What is the importance of triangle congruence in geometry?

Back

Triangle congruence is important in geometry as it allows us to determine that two triangles are identical in shape and size, which is essential for solving problems related to angles, sides, and areas.