Triangle Congruence Theorems

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, 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 triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, 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 triangles are congruent.

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states 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.

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What is the AAA criterion in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which states that if two triangles have equal corresponding angles, they are similar but not necessarily congruent.

Front

Can SSA be used to prove triangle congruence?

Back

No, SSA (Side-Side-Angle) does not guarantee triangle congruence; it can lead to ambiguous cases.

Front

If triangle ABC is congruent to triangle FMN, how would you denote this?

Back

You would denote this as triangle ABC ≅ triangle FMN.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is the angle formed between the two sides being compared, which is crucial for establishing congruence.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruence means the triangles are identical in size and shape, while similarity means they have the same shape but may differ in size.

Front

How can you prove two triangles are congruent using AAS?

Back

To prove two triangles are congruent using AAS, show that two angles and a corresponding non-included side of one triangle are equal to the corresponding parts of the other triangle.