Triangle Congruence Theorems

Front

What does ASA stand for in triangle congruence theorems?

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 is the definition of triangle congruence?

Back

Triangle congruence means that two triangles are identical in shape and size, which can be proven using various theorems.

Front

List the four main triangle congruence theorems.

Back

1. SSS (Side-Side-Side) 2. SAS (Side-Angle-Side) 3. ASA (Angle-Side-Angle) 4. AAS (Angle-Angle-Side)

Front

What does SSS stand for in triangle congruence theorems?

Back

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

Front

What does SAS stand for in triangle congruence theorems?

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 theorems?

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

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 in size.

Front

How can you prove two triangles are congruent using the ASA theorem?

Back

To prove two triangles are congruent using the ASA theorem, you need to show that two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Front

What is the significance of triangle congruence in geometry?

Back

Triangle congruence is significant in geometry because it allows for the determination of equal lengths and angles in various geometric figures, which is essential for solving problems.

Front

Can two triangles be congruent if they have the same angles but different side lengths?

Back

No, two triangles cannot be congruent if they have the same angles but different side lengths; they must have the same size and shape.