Triangle Congruence Theorems

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem 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 theorem 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

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem stating 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, the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem applicable to right triangles stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.

Front

What is the definition of triangle congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

When can you say there is 'not enough information' to prove triangle congruence?

Back

You can say there is 'not enough information' when the given data does not meet the criteria of any triangle congruence theorem.

Front

Provide an example of SSS in triangle congruence.

Back

If triangle ABC has sides of lengths 5 cm, 7 cm, and 9 cm, and triangle DEF also has sides of lengths 5 cm, 7 cm, and 9 cm, then triangle ABC is congruent to triangle DEF by SSS.

Front

Provide an example of SAS in triangle congruence.

Back

If triangle GHI has sides of lengths 4 cm and 6 cm with an included angle of 60 degrees, and triangle JKL has sides of lengths 4 cm and 6 cm with the same included angle, then triangle GHI is congruent to triangle JKL by SAS.

Front

Provide an example of AAS in triangle congruence.

Back

If triangle MNO has angles of 30 degrees and 60 degrees and a side of length 5 cm, and triangle PQR has the same angles and the same side length, then triangle MNO is congruent to triangle PQR by AAS.