Proving Triangle Congruence with ASA and AAS Theorems

What is a congruent statement in the context of triangles?

• A statement that shows two triangles have corresponding sides and angles that are equal.

• A statement that shows two triangles have the same area.

• A statement that shows two triangles are similar.

• A statement that shows two triangles have the same perimeter.

Which theorem states that if all three sides of one triangle are equal to all three sides of another triangle, the triangles are congruent?

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Angle-Side (AAS)

In the Side-Angle-Side (SAS) theorem, where must the angle be located?

• At the midpoint of one side

• At the end of one side

• Outside the two sides

• Between the two sides

What does the Angle-Side-Angle (ASA) theorem require to prove two triangles are congruent?

• Two angles and a side not between them

• Two sides and an angle not between them

• Two angles and the side between them

• Three angles

In the ASA theorem, what is the significance of the side being between the two angles?

• It locks the side into place, making the triangles congruent.

• It ensures the triangles have the same perimeter.

• It ensures the triangles have the same area.

• It ensures the triangles are similar.

What does the Angle-Angle-Side (AAS) theorem require to prove two triangles are congruent?

• Two angles and a side not between them

• Two sides and an angle not between them

• Two angles and the side between them

• Three angles

In the AAS theorem, where is the side located in relation to the two angles?

• At the midpoint of one angle

• Between the two angles

• At the end of one angle

• Outside the two angles

Which of the following combinations does NOT prove triangle congruence?

• Angle-Angle-Side (AAS)

• Angle-Angle-Angle (AAA)

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

Why can't the Angle-Angle-Angle (AAA) combination prove triangle congruence?

• It requires additional information about the angles.

• It only shows similarity, not congruence.

• It does not consider the sides of the triangles.

• It only works for right triangles.

What is a key reason why SSA (Side-Side-Angle) does not prove triangle congruence?

• It requires the sides to be of equal length.

• It does not consider the angles of the triangles.

• It can result in two different triangles.

• It only works for isosceles triangles.