SSS and SAS

Front

What is the SSS Congruence Theorem?

Back

The SSS (Side-Side-Side) Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What is the SAS Congruence Theorem?

Back

The SAS (Side-Angle-Side) Congruence Theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

What does 'included side' mean in triangle congruence?

Back

The included side is the side that is between two angles in a triangle.

Front

If two triangles have two sides of equal length and the included angle is also equal, what can be concluded?

Back

The triangles are congruent by the SAS Congruence Theorem.

Front

If all three sides of triangle ABC are equal to all three sides of triangle DEF, what can be concluded?

Back

Triangle ABC is congruent to triangle DEF by the SSS Congruence Theorem.

Front

What is the difference between SAS and SSS?

Back

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

Front

Can two triangles be congruent if only two angles are known?

Back

Not necessarily; you need at least one side length to use the congruence theorems.

Front

What is an example of using the SSS theorem?

Back

If triangle GHI has sides of lengths 5, 7, and 9, and triangle JKL also has sides of lengths 5, 7, and 9, then GHI is congruent to JKL by SSS.

Front

What is an example of using the SAS theorem?

Back

If triangle MNO has sides of lengths 6 and 8 with an included angle of 60 degrees, and triangle PQR has sides of lengths 6 and 8 with the same included angle, then MNO is congruent to PQR by SAS.

Front

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.