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, the triangles are congruent.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being measured. It is crucial because the congruence is only valid if the angle is between the two sides.

Front

Can two triangles be congruent if only two sides are equal?

Back

No, two triangles cannot be determined to be congruent with only two sides equal unless the included angle is also known (SAS) or all three sides are equal (SSS).

Front

What is a common misconception about triangle congruence?

Back

A common misconception is that two triangles can be congruent if only two angles are equal. This is not sufficient; the sides must also be considered.

Front

If two triangles are not congruent by SSS or SAS, what can be concluded?

Back

If two triangles do not meet the criteria for SSS or SAS, they are not congruent, but further analysis may be needed to explore other congruence criteria.

Front

What is the relationship between congruent triangles and their corresponding parts?

Back

Congruent triangles have corresponding parts (sides and angles) that are equal in measure.

Front

Provide an example of SSS congruence. Triangle ABC has sides of lengths 5 cm, 7 cm, and 9 cm. Triangle DEF has sides of lengths 5 cm, 7 cm, and 9 cm. Are they congruent?

Back

Yes, Triangle ABC and Triangle DEF are congruent by SSS because all three corresponding sides are equal.