Triangle Angle Bisector Theorem Concepts

This video tutorial explains the triangle angle bisector theorem, which states that if a ray bisects an angle of a triangle, it divides the opposite side into segments proportional to the other two sides. The video provides a detailed proof of the theorem by constructing a parallel line and using the triangle proportionality theorem. It also demonstrates the congruence of angles and the properties of isosceles triangles to complete the proof.

What does the Triangle Angle Bisector Theorem state about the segments created by the bisector?

• They are equal in length.

• They are proportional to the other two sides of the triangle.

• They form a right angle.

• They are parallel to each other.

What is the key strategy used to prove the Triangle Angle Bisector Theorem?

• Applying the Law of Sines.

• Constructing a parallel line.

• Using a compass and straightedge.

• Using the Pythagorean Theorem.

What is the purpose of constructing line BE parallel to AD?

• To make the triangle equilateral.

• To bisect the triangle.

• To establish congruent angles through parallel lines.

• To create a right angle.

Which theorem is used to establish the ratio of segments in the proof?

• Angle Sum Theorem

• Law of Cosines

• Pythagorean Theorem

• Triangle Proportionality Theorem

How are angles 1 and 3 related in the proof?

• They are supplementary.

• They are congruent by alternate interior angles.

• They are complementary.

• They are equal by vertical angles.

What role do corresponding angles play in the proof?

• They help establish the congruence of angles 2 and 4.

• They demonstrate that the triangle is scalene.

• They show that the triangle is equilateral.

• They prove that the triangle is right-angled.

How does the Triangle Proportionality Theorem assist in the proof?

• It shows that the triangle is right-angled.

• It establishes the ratio of segments created by the bisector.

• It demonstrates that the triangle is scalene.

• It proves that the triangle is equilateral.

What is the significance of proving that triangle A is isosceles?

• It indicates that the triangle is equilateral.

• It demonstrates that the triangle is right-angled.

• It proves that the base angles are congruent.

• It shows that all sides are equal.

Why is segment AE considered equal to segment AB in the proof?

• Because they are both perpendicular to the base.

• Because they are congruent segments of an isosceles triangle.

• Because they are parallel to each other.

• Because they are both bisected by the angle bisector.

What is the final step in proving the Triangle Angle Bisector Theorem?

• Substituting AE with AB in the ratio.

• Showing that the triangle is equilateral.

• Demonstrating that the triangle is right-angled.

• Proving that all angles are equal.