Congruent Triangles: SSS & SAS

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for 'Side-Side-Side', a method to prove that two triangles are congruent if all three sides of one triangle are equal to the three sides of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for 'Side-Angle-Side', a method to prove that two triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What is the criteria for triangle congruence using SSS?

Back

For SSS, if triangle ABC has sides of lengths a, b, and c, and triangle DEF has sides of lengths d, e, and f, then ABC ≅ DEF if a = d, b = e, and c = f.

Front

What is the criteria for triangle congruence using SAS?

Back

For SAS, if triangle ABC has sides AB and AC with included angle ∠A, and triangle DEF has sides DE and DF with included angle ∠D, then ABC ≅ DEF if AB = DE, AC = DF, and ∠A = ∠D.

Front

Can AAA be used to prove triangle congruence?

Back

No, AAA (Angle-Angle-Angle) cannot be used to prove triangle congruence because it only shows that triangles are similar, not necessarily congruent.

Front

What additional information is needed to prove triangles congruent by SAS?

Back

To prove triangles congruent by SAS, you need to know two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

If two triangles have two pairs of equal sides and the included angle is not equal, are they congruent?

Back

No, if the included angle is not equal, the triangles are not congruent, even if the two pairs of sides are equal.

Front

What is the significance of the included angle in SAS?

Back

The included angle in SAS is crucial because it must be between the two sides being compared; without it, the triangles may not be congruent.

Front

How can you determine if two triangles are congruent using SSS?

Back

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

Front

How can you determine if two triangles are congruent using SAS?

Back

Measure two sides and the included angle of both triangles. If the two sides and the included angle are equal, then the triangles are congruent by SAS.