SSS/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 significance of congruent triangles in geometry?

Back

Congruent triangles have the same shape and size, which means their corresponding sides and angles are equal. This property is essential in proving other geometric theorems and solving problems.

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 for the triangles to be congruent.

Front

What is the difference between SSS and SAS?

Back

SSS requires all three sides to be equal for congruence, while SAS requires two sides and the included angle to be equal.

Front

If two triangles are not congruent, what can be said about their sides and angles?

Back

If two triangles are not congruent, at least one pair of corresponding sides or angles is not equal.

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 sides are equal.

Front

Provide an example of SAS congruence. Triangle GHI has sides of lengths 6 cm, 8 cm, and an included angle of 60 degrees. Triangle JKL has sides of lengths 6 cm, 8 cm, and an included angle of 60 degrees. Are they congruent?

Back

Yes, Triangle GHI and Triangle JKL are congruent by SAS because two sides and the included angle are equal.