SAS & SSS

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a criterion for triangle congruence that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence that states if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

When can triangles be considered congruent by SSS?

Back

Triangles can be considered congruent by SSS when all three corresponding sides of the triangles are equal in length.

Front

When can triangles be considered congruent by SAS?

Back

Triangles can be considered congruent by SAS when two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle.

Front

What does it mean if two triangles are 'not necessarily congruent'?

Back

'Not necessarily congruent' means that the triangles may not be equal in size and shape, even if some sides or angles are equal.

Front

Provide an example of SAS congruence.

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

Provide an example of SSS congruence.

Back

If triangle GHI has sides GH = 4 cm, HI = 6 cm, and GI = 8 cm, and triangle JKL has sides JK = 4 cm, KL = 6 cm, and JL = 8 cm, then triangles GHI and JKL are congruent by SSS.

Front

What is the importance of congruence in geometry?

Back

Congruence is important in geometry because it allows us to determine that two shapes are identical in size and shape, which is essential for solving problems related to measurements, constructions, and proofs.

Front

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

Back

No, two triangles cannot be considered congruent if only one side is equal; at least two sides and the included angle (SAS) or all three sides (SSS) must be equal.

Front

What is the relationship between angles and sides in SAS?

Back

In SAS, the angle must be included between the two sides that are being compared; this means it is the angle formed by the two sides.