Triangle Congruence Theorems and Conditions

The video tutorial introduces triangle congruence, explaining various congruence theorems such as side-side-side, side-angle-side, hypotenuse-leg, angle-side-angle, and angle-angle-side. Through multiple examples, the teacher demonstrates how to determine if triangles are congruent and how to create congruent triangles by adding necessary parts.

What is the primary condition for two triangles to be congruent using the Side-Side-Side (SSS) theorem?

• Two angles and the included side are equal.

• Two sides and the included angle are equal.

• All three angles are equal.

• All three sides are equal.

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

• It must be an exterior angle.

• It must be the angle between the two sides.

• It must be the smallest angle.

• It must be the largest angle.

Why can't the Side-Side-Angle (SSA) condition be used to prove triangle congruence?

• It does not guarantee congruence.

• It requires all angles to be equal.

• It only applies to right triangles.

• It requires all sides to be equal.

Which theorem is specifically used for proving congruence in right triangles?

• Angle-Side-Angle (ASA)

• Hypotenuse-Leg (HL)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

In the Angle-Side-Angle (ASA) theorem, where is the side located?

• Between the two angles

• Opposite the largest angle

• Adjacent to the smallest angle

• Outside the triangle

What additional information is needed to prove congruence using the Angle-Angle-Side (AAS) theorem?

• The side opposite the smallest angle

• A third angle

• A third side

• The side opposite the largest angle

When given two sides of a triangle, what additional part is needed to use the Side-Side-Side (SSS) theorem?

• An angle between the sides

• An angle opposite one of the sides

• A perpendicular height

• A third side

In a problem requiring Side-Angle-Side (SAS) congruence, what must be true about the angle?

• It must be the largest angle.

• It must be the smallest angle.

• It must be between the two given sides.

• It must be an exterior angle.

What is the missing element needed to prove congruence using the Hypotenuse-Leg (HL) theorem?

• The other leg

• The other hypotenuse

• The angle opposite the hypotenuse

• The angle adjacent to the hypotenuse

Which theorem can be used if two angles and a non-included side are known?

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)