Angle Angle Side Theorem Concepts

The video tutorial explains the Angle Angle Side (AAS) congruence theorem, which states that 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. The video uses diagrams to illustrate the theorem and provides an example to demonstrate how AAS can be used to prove triangle congruence. It also explains why AAS works by relating it to the Angle Side Angle (ASA) theorem.

What does the Angle Angle Side Congruence Theorem state?

• Two triangles are congruent if two angles and a non-included side are congruent.

• Two triangles are congruent if all three angles are congruent.

• Two triangles are congruent if two angles and the included side are congruent.

• Two triangles are congruent if all three sides are congruent.

In the Angle Angle Side Congruence Theorem, what must be congruent between two triangles?

• Two sides and one angle

• Two angles and one side

• Three sides

• Three angles

What is the primary focus of the Angle Angle Side theorem?

• Congruence of two angles and a non-included side

• Congruence of two sides and an included angle

• Congruence of all sides

• Congruence of all angles

What is the significance of the non-included side in the Angle Angle Side theorem?

• It is not necessary for congruence.

• It is the side between the two angles.

• It is the side not between the two angles.

• It is the longest side of the triangle.

Which of the following is NOT a requirement for the Angle Angle Side theorem?

• The side must be non-included.

• The side must be included between the angles.

• One side must be congruent.

• Two angles must be congruent.

Which theorem helps to establish the third angle's congruence in the Angle Angle Side theorem?

• Third Angle Theorem

• Angle Bisector Theorem

• Pythagorean Theorem

• Side Angle Side Theorem

How does the Angle Angle Side theorem relate to the Angle Side Angle theorem?

• They are unrelated.

• They both require three angles to be congruent.

• Angle Angle Side is a special case of Angle Side Angle.

• Angle Side Angle is a special case of Angle Angle Side.

How does the Third Angle Theorem assist in the Angle Angle Side theorem?

• It proves the triangles are identical.

• It proves the triangles are similar.

• It proves the third angle is congruent.

• It proves all sides are congruent.

What is the relationship between the Angle Angle Side and Angle Side Angle theorems?

• They both require three angles to be congruent.

• They both require two angles to be congruent.

• They both require two sides to be congruent.

• They are completely different.

What is the role of vertical angles in proving congruence in the example problem?

• They are used to prove the triangles are similar.

• They help establish congruence of a third angle.

• They are not used in the proof.

• They are used to find the length of a side.