Geometry 4.3 SSS and SAS

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

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

Front

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

Back

To determine if two triangles are congruent using SSS, measure the lengths of all three sides of both triangles. If all three pairs of corresponding sides are equal, the triangles are congruent.

Front

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

Back

To determine if two triangles are congruent using SAS, measure two sides and the included angle of both triangles. If the two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle, they are congruent.

Front

What is the difference between SSS and SAS in triangle congruence?

Back

The difference is that SSS requires all three sides to be equal, while SAS requires two sides and the angle between them to be equal.

Front

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

Back

No, two triangles cannot be 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 significance of the included angle in SAS?

Back

The included angle in SAS is the angle formed between the two sides being compared. It is crucial because it ensures that the triangles are not only the same shape but also the same size.

Front

If two triangles have two equal sides and a non-included angle, are they congruent?

Back

No, if two triangles have two equal sides and a non-included angle, they are not necessarily congruent. This is known as the SSA condition, which does not guarantee congruence.

Front

What is the SSA condition in triangle congruence?

Back

The SSA condition refers to having two sides and a non-included angle equal in two triangles. This condition does not guarantee that the triangles are congruent.

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates that two figures are congruent, often written in the form of triangle names, such as triangle ABC ≅ triangle DEF.