Triangle Congruence and Angle Bisector Theorem

This video tutorial explains the angle bisector theorem, which states that a point on the angle bisector is equidistant from the sides of the angle. The video provides a visual representation and a detailed proof using congruent triangles. The proof is structured in a two-column format, demonstrating the congruence of triangles by angle, angle, side. The tutorial concludes by reinforcing the theorem's application, showing that any point on the angle bisector results in two congruent triangles, confirming the point's equidistance from the angle's sides.

What does the angle bisector theorem state about a point on the angle bisector?

• It is closer to one side of the angle.

• It is equidistant from the sides of the angle.

• It is at the midpoint of the angle.

• It forms a right angle with the bisector.

What is the main strategy used to prove the angle bisector theorem?

• Using coordinate geometry.

• Using the Pythagorean theorem.

• Applying the law of sines.

• Proving congruence of triangles.

Which method is used to prove the congruence of triangles in the theorem?

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

• Side-Angle-Side (SAS)

Which property is used to show that two angles are right angles in the proof?

• Vertical angles theorem.

• Alternate interior angles.

• Supplementary angles.

• Definition of perpendicular lines.

What is the significance of the angle bisector in the proof?

• It divides the angle into two unequal parts.

• It is perpendicular to the base.

• It forms an obtuse angle.

• It divides the angle into two equal parts.

What does the reflexive property state in the context of the proof?

• A segment is equal to another segment.

• An angle is equal to itself.

• A segment is equal to itself.

• An angle is equal to another angle.

Why are the right angles considered congruent in the proof?

• Because they are adjacent.

• Because all right angles are congruent.

• Because they are supplementary.

• Because they are complementary.

What is the role of the shared side in proving triangle congruence?

• It is ignored in the proof.

• It is used to show similarity.

• It is used to show parallelism.

• It is used to show congruence by the reflexive property.

What is the final conclusion of the angle bisector theorem proof?

• The segments are congruent.

• The triangles are not congruent.

• The segments are not equal.

• The point is not equidistant.

What does the conclusion of the proof confirm about the angle bisector theorem?

• It confirms the equidistance of points on the bisector.

• It is only applicable to obtuse angles.

• It confirms the inequality of segments.

• It is only applicable to acute angles.