Triangle Congruence Theorems

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the AAS theorem stand for?

Back

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

Front

What does the SSS theorem stand for?

Back

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

Front

What does the SAS theorem stand for?

Back

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does the HL theorem stand for?

Back

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

Front

What is the definition of the ASA theorem?

Back

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

Front

How can you denote triangle congruence?

Back

Triangle congruence can be denoted using the symbol '≅'. For example, if triangle ABC is congruent to triangle DEF, it can be written as triangle ABC ≅ triangle DEF.

Front

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

Back

To prove triangles are congruent by AAS, you need to know two angles and one non-included side of one triangle are congruent to the corresponding parts of another triangle.

Front

What is the difference between SSA and congruence theorems?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence because the angle is not included between the two sides, leading to the possibility of two different triangles.

Front

What is the significance of the congruence symbol '≅'?

Back

The congruence symbol '≅' indicates that two geometric figures, such as triangles, are congruent, meaning they have the same shape and size.