Exploring Congruent Triangle Theorems

What is an included angle in a triangle?

• An angle that is equal to 90 degrees

• An angle that is not between two sides

• An angle formed by two sides

• An angle that is outside the triangle

Which side is considered the included side for angles B and C in a triangle?

• None of the above

• BC

• AC

• AB

What does the Side-Side-Side (SSS) postulate state?

• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

• If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, the triangles are congruent.

• If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

• If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

In the Side-Angle-Side (SAS) postulate, what must be true about the angle?

• The angle must be the largest angle in the triangle.

• The angle must be a right angle.

• The angle must be between the two sides.

• The angle must be an exterior angle.

What does the Angle-Side-Angle (ASA) postulate state?

• If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, the triangles are congruent.

• If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

• If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

• If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

What is the difference between ASA and AAS postulates?

• ASA requires the side to be between the two angles, while AAS does not.

• ASA requires three sides to be congruent, while AAS requires two angles and a side.

• ASA requires the angles to be right angles, while AAS does not.

• ASA requires the angles to be exterior angles, while AAS requires them to be interior angles.

Which postulate is used specifically for right triangles?

• ASA

• HL

• SAS

• SSS

Why does the Angle-Angle-Angle (AAA) postulate not prove triangle congruence?

• Because it only proves similarity, not congruence.

• Because it requires three sides to be congruent.

• Because it requires the angles to be right angles.

• Because it requires the angles to be exterior angles.

What is the reflexive property in the context of triangle congruence?

• A property that states a side is equal to itself.

• A property that states two angles are equal.

• A property that states an angle is equal to itself.

• A property that states two sides are equal.

What can be inferred if two triangles share a common side?

• The common side is not considered in congruence.

• The common side is congruent to itself by the reflexive property.

• The triangles are not congruent.

• The triangles are similar.