Triangle Congruence Theorems

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for 'Side-Side-Side'. It is a theorem that states if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for 'Side-Angle-Side'. It is a theorem that states 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 ASA stand for in triangle congruence?

Back

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

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for 'Angle-Angle-Side'. It is a theorem that states if two angles and a non-included side of one triangle are equal to two angles and a corresponding non-included side of another triangle, then the two triangles are congruent.

Front

What does HL stand for in triangle congruence?

Back

HL stands for 'Hypotenuse-Leg'. It is a theorem that applies 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, then the two triangles are congruent.

Front

Which triangle congruence theorem is NOT valid?

Back

AAA (Angle-Angle-Angle) is NOT a valid triangle congruence theorem because it does not guarantee that the triangles are congruent; it only shows that they are similar.

Front

What additional information is needed to prove two triangles are congruent by SAS?

Back

To prove two triangles are congruent by SAS, you need to know that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

If two triangles have two pairs of equal angles, what can be concluded?

Back

If two triangles have two pairs of equal angles, they are similar, but not necessarily congruent unless the third side is also equal.

Front

What is the relationship between congruence and similarity in triangles?

Back

Congruent triangles are similar, but similar triangles are not necessarily congruent. Congruent triangles have the same size and shape, while similar triangles have the same shape but may differ in size.

Front

How can you prove triangles are congruent using the SSS theorem?

Back

To prove triangles are congruent using the SSS theorem, you must show that all three sides of one triangle are equal to all three sides of another triangle.